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IHE  EFFICIENCY  OF  COLLEGE  STUDENTS 

AS  RELATED  TO  AGE  AT  ENTRANCE 

AND  SIZE  OF  HIGH  SCHOOL 


A  DISSERTATION 

SUBMITTED  TO  THE  FACULTY 

OF  THE  GRADUATE  SCHOOL  OF  ARTS  AND  LITERATURE 

IN  CANDIDACY  FOR  THE  DEGREE  OF 

DOCTOR  OF  PHILOSOPHY 

(Department  of  Education) 

V  ^    .  ^  a  A  ^  y/-%. 


V*'  "^  J^     "^V 


(OF  THE 
Wl^IVEkSITY 


BY 

Benjamin  Floyd  Pittenger 


PUBLIC  SCHOOL  PUBLISHING  COMPANY 

BLOOMINGTON,  ILLINOIS 

1917 


EXCHANGE 


Digitizad  by  the  Internet  Archive 

in  2007  with  funding  from 

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Ube  TUntrersttp  ot  Cbicaao 


THE  EFFICIENCY  OF  COLLEGE  STUDENTS 

AS  RELATED  TO  AGE  AT  ENTRANCE 

AND  SIZE  OF  HIGH  SCHOOL 


A  DISSERTATION 

SUBMITTED  TO  THE  FACULTY 

OF  THE  GRADUATE  SCHOOL  OF  ARTS  AND  LITERATURE 

IN  CANDIDACY  FOR  THE  DEGREE  OF 

DOCTOR  OF  PHILOSOPHY 

(Department  of  Education) 


BY 

Benjamin  Floyd  Pittenger 


PUBLIC  SCHOOL  PUBLISHING  COMPANY 

BLOOMINGTON,  ILLINOIS 

1917 


^Or 


^\t 


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^-^^^ 


Copyright  1917  By 

Guy  M.  Whipplk 

secretary  of  the  society 


All  Right  Reserved 


Published  August,  1917 


r://*, ; 


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,.      i  J  w  -•         J  J 


OFFICERS  OF  THE  NATIONAL  SOCIETY  FOR  THE 
STUDY  OF  EDUCATION 


President 

Lotus  D.  Coffman 
University  of  Minnesota,  Minneapolis,  Minnesota 

Vice-President 

J.  A.  C.  Chandler 
Superintendent  of  Schools,  Richmond,  Virginia 

Secretary -Treasurer 

Guy  M.  Whipple 
University  of  Illinois,  Urbana,  Illinois 

Executive  Committee 

Harry  B.  Wilson  (1918) 
Superintendent  of  Schools,  Topeka,  Kansas 

DwiGHT  B.  Waldo  (1919) 
State  Normal  School,  Kalamazoo,  Michigan 

H.  Lester  Smith  (1920) 
Indiana  University,  Bloomington,  Indiana 

Ernest  Horn  (1921) 
State  University  of  Iowa,  Iowa  City,  Iowa 


37^9'/'^ 


Board  of  Trustees 

S.  Chester  Parker  (1918) 
University  of  Chicago,  Chicago,  Illinois 

Edward  C.  Elliott  (1919) 
University  of  Montana,  Helena,  Montana 

George  Melcher  (1920) 
Bureau  of  Research  and  Efficiency,  Kansas  City,  Missouri 


TABLE  OF  CONTENTS 

PAoa 

Editor's  Preface 7 

Author's  Preface 8 

Introduction 9 

Chapter  I.    Methods  in  Earlier  Studies  Based  Upon  School 

AND  College  Marks 13 

Earlier  Studies  of  Distribution.  . . . : 13 

Studies  of  Continuity — Steps  in  the  Procedure,  . .  15 
Studies  of  Comparison 23 

Chapter  II.     Earlier  Studies  Concerned  with  Age  at  En- 
trance AND  with  Size  of  High  School 25 

Age  at  Entrance  into  the  Elementary  School.  . .  25 

Age  at  Entrance  into  the  High  School 31 

^J^GE  AT  Entrance  into  College 35 

Studies  Concerned  with  Size  of  High  School 35 

Chapter  III.    Materials  and  Methods 42 

Evaluation  of  Materials 43 

Methods  of  Studying  College  Materials 47 

Chapter  IV.   ^Entrance  Age  as  Related  to  College  Effi- 
ciency    55 

^Comparison  of  Groups  Entering  at  Different  Ages  56 

Tables  Showing  Differences 58 

Graphs  Showing  Differences 67 

Relation  Shown  by  Elimination  and  Retention 70 

Summary 76 

Chapter  V.    Normal,    Pre-Normal    and    Pqst-Normal    En- 
trance Ages  78 

jComparative  College  Efficiency 

^s  Measured  by  Scholarship  Marks 79 

^s  Measured  by  Retention  and  Elimination 83 

Summary 87 


PAQl 

Chapter  VI.    A  Partial  Explanation 88 

^Entrance  Ages  as  Related  to  Immediacy  of  College 

Entrance 89 

Age  and  Immediacy  as  Related  to  High   School 

Scholarship 92 

^uomparison  of  identical  students  in  high  school 

AND  College 93 

Conclusions 95 

Chapter  VII.    Size  of  High  School  as  Related  to  Efficiency 

in  College   98 

As  Related  to  College  Scholarship 98 

As  Related  to  College  Retention 101 

As  Related  to  High-School  Scholarship 104 

^s  Related  to  College  Efficiency  105 

Summary 110 

Chapter  VIII.    General  Summary Ill 


EDITOR'S   PREFACE 

The  study  presented  herewith  by  Mr.  Pittenger,  of  the  Uiliver- 
sity  of  Texas,  was  carried  on  by  him  while  he  was  a  member  of  the 
instructional  staff  of  the  University  of  Minnesota  and  has  been 
accepted  as  a  thesis  for  the  doctorate  degree  at  the  University  of 
Chicago. 

The  problem  is  one  of  both  academic  and  practical  interest: 
is  the  quality  of  work  done  by  the  young  men  and  women  who 
enter  our  colleges  affected  by  the  age  at  which  they  enter  or  by 
the  size  of  the  high  school  from  which  they  come? 

Our  readers  will  find  the  problem  set  forth  clearly  in  the 
introductory  chapter  and  a  summary  of  the  conclusions  in  the  last 
chapter.  The  detailed  presentation  of  the  method  of  study  and  of 
the  materials  on  which  the  conclusions  are  based  will  be  found  in 
the  intervening  chapters. 

G.  M.  W. 


AUTHOR'S  PREFACE 

In  the  chapters  which  follow,  and  which  report  the  results  of 
a  statistical  study  of  some  problems  connected  with  high-school  and 
college  administration,  the  writer  has  tried  to  meet  the  demands  of 
two  very  different  classes  of '  educational  workers.  On  the  one 
hand  are  high-school  and  college  instructors  and  administrators, 
whose  interests  are  centered  in  practical  results.  On  the  other  hand 
are  educational  investigators,  who  are  interested  in  the  accumulation 
of  a  comprehensive  and  well-organized  body  of  reliable  information, 
and  who  will  properly  insist  upon  a  detailed  presentation  of  all 
of  the  data  and  methods  underlying  the  conclusions  reached. 

The  writer's  obligations  are  many.  He  is  indebted  to  the 
managers  of  the  research  fund  of  the  University  of  Minnesota  for 
financial  assistance  in  securing  the  scholarship  records  of  the  college 
students  surveyed.  Dr.  George  F.  James,  former  dean  of  the 
College  of  Education  of  the  University  of  Minnesota,  gave  much 
encouragement  and  assistance  in  the  initial  stages  of  the  enterprise. 
Director  Charles  H.  Judd  and  Dr.  H.  0.  Rugg,  of  the  School  of 
Education  of  the  University  of  Chicago,  have  contributed  the  most 
careful  criticism  and  have  assisted  in  preparing  the  manuscript 
for  the  press.  Finally,  the  writer  would  express  his  particular 
obligations  to  the  superintendents  and  principals  of  high  schools 
in  Minnesota  and  adjoining  states,  whose  laborious  transcription 
of  the  high-school  records  of  thousands  of  pupils  was  indispensable 
to  the  successful  consummation  of  the  work. 

B.  F.  P. 


THE  EFFICIENCY  OF  COLLEGE  STUDENTS  AS  CONDI- 
TIONED BY  AGE  AT  ENTRANCE   AND   SIZE 
OF  HIGH  SCHOOL 

INTRODUCTION 

STATEMENT   OF  PROBLEMS 

This  study  seeks  mainly  to  evaluate  two  factors  in  the  efficiency 
shown  as  students  in  the  College  of  Science,  Literature,  and  the 
Arts  at  the  University  of  Minnesota,  by  828  graduates  of  that 
uninversity's  tributary  high  schools.  The  factors  considered  are 
the  ages  at  which  these  pupils  entered  upon  their  college  work,  and 
the  size  and  general  characteristics  of  the  high  schools  from  which 
they  came.    The  principal  problems  are  as  follows : 

1.  What  entrance  ages  were  correlated  with  the  highest  degree 
of  college  efficiency  ?    How  may  these  correlations  be  explained  ? 

2.  To  what  extent  did  the  scholarship  records  of  the  college 
students  show  correlation  with  the  number  of  pupils  enroled,  and 
with  the  number  of  pupils  per  teacher,  in  the  high  schools  from 
which  they  came  ?    How  can  one  best  explain  these  relations  ? 

The  writer  would  acknowledge  at  the  outset  that  the  factors, 
the  influence  of  which  upon  college  efficiency  he  seeks  to  discover, 
are  very  broad  and  complex.  Today,  for  instance,  there  is  a 
tendency  to  substitute  the  study  of  physiological  for  that  of  chro- 
nological age,  i.  e.,  actual  bodily  maturity  for  ages  in  years  and 
months;  at  least  to  emphasize  the  fact  that  chronological  age  is  a 
very  imperfect  index  of  physical  and  mental  maturity.  To  this 
tendency  the  study  of  chronological  entrance  ages  in  the  present 
investigation  is  apparently  opposed.  But  a  review  of  the  studies 
thus  far  made  upon  the  relations  obtaining  between  chronological 
and  anatomical  ages  shows  them,  as  at  present  defined,  to  be  prac- 
tically coincident  after  the  chronological  age  of  seventeen.^     As 


'Bee  Chapter  II,  Section  2. 


10  THE  SIXTEEN TE  YEARBOOK 

almost  all  college  students  enter  at  seventeen  or  later  the  issue 
raised  is  not- important.  Furthermore,  as  the  study  proceeds,  it 
will  appear  that  other  causes  than  differences  in  maturity  are 
adduced  to  account  for  the  phenomena  discovered. 

As  to  the  second  factor,  it  is  probable  that  the  size  of  a  high 
school  exercises  only  an  indirect  influence  upon  the  college  efficiency 
of  its  graduates,  through  other  more  vital  factors  which  are 
correlated  with  it.  The  size  is  but  the  sign  of  their  presence  or 
absence.  A  large  school,  for  instance,  is  generally  better  equipped 
than  a  small  school,  and  usually  employs  teachers  with  broader 
training  and  experience.^  Both  of  these  facts,  and  probably  others, 
should  make  for  the  higher  efficiency  of  its  graduates  in  college. 
On  the  other  hand  the  small  school  is  usually  characterized  by 
smaller  classes,^  and  thus  affords  better  opportunity  for  individual 
attention.  Enough  has  been  said  to  establish  the  rather  obvious 
point  that  the  phrase  ''size  of  high  school"  is  a  blanket  expression; 
that  size  in  itself  is  not  effective,  but  that  it  is  significant  because 
of  other  factors  which  are  connected  with  it. 

From  this  point  of  view  an  intensive  study  of  the  relation 
existent  between  the  size  of  a  high  school  and  the  college  efficiency 
of  its  graduates  looks  like  wasted  effort.  But  to  the  school  and 
college  administrator,  size  is  a  criterion  easy  to  ascertain,  and  if 
a  consistent  relation  between  these  variables  can  be  established,  the 
results  promise  to  serve  administrative,  if  not  scientific  ends. 

Two  measures  of  college  efficiency  are  utilized  in  this  investiga- 
tion; first,  comparative  rank  in  scholarship  as  indicated  by  the 
marks  received;  and  second,  the  length  of  time  spent  in  college 
work.  An  efficient  student  is  one  who  does  good  work,  and  who 
remains  to  complete  his  college  course.  In  fact,  scholarship  and 
retention  are  regarded,  not  merely  as  criteria  of  college  efficiency, 
but  as  constituting  that  efficiency  in  the  meaning  of  the  present 
study.  Efficiency  is  synonymous  with  good  scholarship  and  with 
persistency  to  the  end.  By  taking  this  position,  the  author  pro- 
poses to  avoid  an  unprofitable  and  vexatious  discussion  of  the 


^Coffman,  L.  D.    The  Social  Composition  of  the  Teaching  Population. 
"Judd,  C.  H.,  and  Counts,  G.  S.     Study  of  the  Colleges  and  High  Sehools 
of  the  North  Central  Association.    Bull.  Bureau  of  Education,  1915,  No.  6. 


INTBODUCTION  H 

ultimate  significance  of  both  criteria,  particularly  of  school  and 
college  scholarship  marks. 

Through  its  measurement  of  efficiency  in  terms  of  marks  and 
retention  this  investigation  is  allied  with  two  rather  extensive 
groups  of  previous  studies.  The  first  group  comprises  the  numer- 
ous investigations  based  upon  school  and  college  marks ;  the  second, 
the  equally  numerous  investigations  of  elimination  and  retention. 
Perusal  of  the  many  papers  dealing  with  these  subjects,  particu- 
larly those  based  upon  school  marks,  reveals  a  grave  need  for  a 
summary  of  the  methods  pursued,  looking  toward  careful  criticism 
and  ultimate  standardization.  The  reader  becomes  amazed  at  the 
great  variety  of  methods  used  to  achieve  very  similar  ends,  and 
at  the  even  greater  differences  in  reliability  which  these  methods 
display.  Probably  no  absolute  standardization  of  method  is  either 
possible  or  desirable.  Doubtless  capable  students  will  continue  to 
differ  as  to  the  virtues  of  certain  forms  of  procedure.  But  the 
evidences  of  grossly  amateurish  investigation  ought  to  disappear; 
the  conclusions  which  have  followed  from  hasty  labor  should  be 
pointed  out,  and  no  small  part  of  the  work  which  has  been  per- 
formed probably  will  have  to  be  repeated.  Preliminary  to  that 
process  we  must,  so  far  as  possible,  standardize  our  methods. 

With  some  diffidence  the  writer  presumes  to  offer  a  summary 
of  the  methods  heretofore  employed  in  studies  of  marks  and  to 
point  out  what  appear  to  be  the  more  obvious  types  of  error,  with 
suggestions  for  their  correction.  The  first  chapter  of  the  monograph 
is  devoted  to  this  purpose. 


CHAPTER  I 

METHODS  PURSUED  IN  EARLIER  STUDIES  BASED  UPON 
SCHOOL  AND  COLLEGE  MARKS 

A  review  of  the  methods  pursued  in  the  various  studies  of 
school  and  college  marks  necessitates  a  classification  of  these  studies 
according  to  the  nature  of  the  problems  which  they  attack.  From 
this  point  of  view  they  fall  readily  into  three  fairly  distinct  classes, 
which  may  be  described  as  (1)  studies  of  distribution,  (2)  studies 
of  continuity,  and  (3)  studies  of  comparison.  In  some  investiga- 
tions more  than  one  of  these  types  of  problem  may  appear,  but  none 
has  been  observed  which  introduced  marking  problems  of  a  dif- 
ferent sort. 

Section  1 
studies  of  distribution 

Definition.  Under  this  title  may  be  included  those  studies 
which  have  sought  chiefly  to  determine  whether  or  not  the  curve 
representing  the  distribution  of  scholarship  marks  follows  the  form 
of  the  binomial  or  normal  curve  that  presumably  represents  the 
distribution  of  biological  traits  generally.  As  a  rule,  these  studies 
have  been  conducted  by  persons  interested  in  defending  or  opposing 
the  theory  that  pupils  should  be  graded  in  their  school  achievement 
according  to  their  rank  among  their  classmates,  rather  than  by 
comparison  with  some  intangible  standard  of  ideal  accomplishment. 
With  the  recent  development  of  objective  scales  for  the  measure- 
ment of  efficiency  in  school  subjects,  the  necessity  for  arguments 
and  studies  of  this  character  has  considerably  declined.  For  this 
reason,  and  because  these  studies  have  little  bearing  upon  our  own 
set  of  problems,  our  summary  of  methods  in  this  field  is  very  brief  .^ 

Methods.  The  methods  which  have  generally  been  pursued  in 
studies  of  this  character  comprise  three  steps. 


^For  a  review  of  results  of  studies  of  distribution  see  Rugg,  H.  O.,  Teachers ' 
marks  and  marking  systems.  Educational  Administration  and  Supervision,  Vol. 
I,  117-142.  Also  Pittenger,  B.  F.,  Scientific  studies  of  the  marking  system, 
American  Schoolmaster,  April,  1915,  145-157. 

13 


14  TRE  SIXTEENTH  YEAEBOOK 

1.  Where  schools  with  different  marking  scales  are  included 
in  one  study,  these  different  scales  usually  must  be  reduced  to  com- 
parable units.  Those  ordinarily  met  with  are  the  percentage  and 
the  letter  scales.  In  the  reduction  of  these  to  comparable  bases  the 
following  points  must  be  kept  in  mind : 

(a)  The  letter  scale  may  be  converted  into  a  percentage  scale 
by  properly  weighting  each  of  its  component  divisions.  Similarly, 
the  percentage  scale  may  be  changed  into  a  letter  scale  by  repre- 
senting certain  ranges  of  percentage  marks  by  letter  units. 

(b)  Where  scales  with  different  passing  marks  are  embraced 
in  one  study  some  readjustment  may  be  necessary.  Few,  if  any, 
more  students  are  failed  in  schools  with  a  passing  mark  of  70  than 
in  schools  with  a  passing  mark  of  60.  Conseqently,  the  marks  of 
such  schools  can  be  regarded  as  comparable  only  when  those  of  the 
schools  possessing  the  lower  passing  marks  have  been  properly 
weighted.  One  method  which  has  been  used  for  this  purpose  is  to 
weight  marks  of  the  schools  with  the  lower  passing- marks,  by  adding 
to  each  an  amount  equal  to  the  difference  between  the  median 
marks  of  each  type  of  school.^ 

2.  The  second  step  consists  in  collecting  the  marks  into  unit 
groups.  The  nature  of  these  groups  depends  upon  the  marking 
scale  involved,  as  well  as  upon  the  nature  of  the  problem.  Where 
the  letter  scale  is  used  the  method  is  usually  the  simple  one  of  de- 
termining the  number  of  pupils  to  whom  each  letter  has  been 
assigned.  Where  the  percentage  scale  is  employed  the  marks  may 
be  collected  into  percentile  groups,  or  into  groups  of  five  or  tens. 
The  first  is  the  more  common  mode  in  studies  of  this  kind. 

3.  The  third  step  consists  in  plotting  a  curve  to  represent  the 
form  of  the  distribution.  Here  distances  on  the  abscissa  represent 
the  marking  units,  with  the  higher  units  usually  toward  the  right- 
hand  side  of  the  graph.  This  direction  has  been  reversed  by  a  few 
students.  Distances  on  the  ordinate  represent  the  number  of  cases 
comprised  within  each  marking  unit. 

The  majority  of  distribution  studies  are  complete  at  this  point, 
or  after  comparison  of  the  actual  distribution  with  the  theoretical 


^Starcli,  D.   and   Elliott,   E.   C.     Reliability   of   grading  in  mathematics. 


School  Eeview,  Vol.  21,  254r-259 


METHODS  PUBSUED  IN  EABLIEB  STUDIES  15 

curve.  But  a  few  studies,  possessing  peculiar  aims,  have  gone 
further  in  their  analysis.  The  methods  in  these  cases  are  usually- 
appropriate  only  to  the  special  problems  raised.  Those  which  are 
capable  of  extended  application  are  described  in  the  sections  which 
follow. 

Section  2 

studies  of  continuity 

Definition.  Under  this  head  are  to  be  grouped  all  of  those 
studies  which  aim  principally  to  compare  the  school  efficiency  of  a 
pupil  or  a  group  of  pupils  in  one  school  subject  or  at  one  stage  of 
schooling  with  the  efficiency  of  the  same  pupil  or  group  of  pupils  in 
another  subject  or  at  another  stage  of  schooling.  The  essential  thing 
is  that  the  same  students'  records  are  compared,  not  those  of  dif- 
ferent students. 

Two  general  types  of  continuity  studies  are  to  be  recognized. 
The  first  is  concerned  with  the  maintenance  of  scholarship  rank  in 
passing  from  the  elementary  to  the  high  school  or  from  the  high 
school  to  the  college,  and  from  one  to  another  of  the  succeeding 
school  and  college  years.  The  second  has  reference  to  the  correla- 
tion of  abilities  manifested  by  the  same  pupils  in  different  school 
subjects.3 

Metliods.    We  may  note  the  following  steps  in  the  procedure : 

1.  The  first  step  raises  the  question  of  the  proper  quantity  of 
materials  upon  which  such  a  study  should  be  based.  Two  prac- 
tices are  noteworthy.  The  majority  of  investigators  have  sought 
for  large  quantities  of  marks,  trusting  to  numbers  to  equalize  errors 
due  to  differences  in  the  conditions  under  which  these  marks  were 
received.^  A  few,  however,  have  stressed  the  point  of  similarity 
of  conditions,  and  have  held  that  a  limited  number  of  cases  for 
which  such  similarity  can  be  proved  is  preferable  to  a  larger  number 
regarding  whom  these  facts  are  not  definitely  known.^    Both  types 


'For  a  review  of  results  of  continuity  studies,  see  Pittenger,  B.  F.  Studies 
based  upon  school  and  college  marks.  American  Schoolmaster:  May,  1915, 
207-219. 

*See,  for  instance,  Dearborn,  W.  F.  Belative  Standing  of  Pupils  in  the 
High   School   and    University.     Bulletin,   University   of   Wisconsin,   No.    312. 

'Frailey,  J.  E.,  and  Grain,  C.  M.  Correlations  of  excellence  in  different 
school  subjects.    Journal  of  Educational  Psychology,  Vol.  5,  141-154. 


Ig  THE  SIXTEENTH  YEARBOOK 

of  study  are  valuable,  and  if  their  results  coincide,  the  validity  of 
their  combined  conclusions  seems  reasonably  assured. 

2.  The  problem  of  the  subject-unit  versus  the  hour-unit  may 
next  be  raised.  Shall  a  mark  in  one  subject  be  regarded  as  equal 
in  value  to  the  same  mark  in  any  other  subject,  regardless  of  the 
number  of  hours  per  week  devoted  to  each?  Or  shall  the  mark 
in  each  subject  be  weighted  according  to  the  number  of  hours  in- 
volved? Only  one  study  has  been  noted  in  which  this  problem  has 
been  definitely  raised  and  the  latter  procedure  adopted.^  Doubtless, 
the  prevailing  practice  is  more  or  less  warranted  by  the  fact  that 
in  the  great  majority  of  courses  the  number  of  hours  involved  is 
identical,  and  by  the  principle  that  subjects  with  more  than  the 
usual  number  of  hours  in  general  compensate  for  those  with  less. 
However,  the  problem  here  designated  should  be  kept  in  mind,  and 
the  probable  extent  of  the  error  involved  should  always  be  estimated. 

3.  In  the  third  place,  care  should  always  be  exercised  that  the 
cases  chosen  are  representative,  and  are  not  so  selected  as  to  in- 
validate the  conclusions  based  upon  them. 

4.  Too  many  of  the  earlier  studies  of  school  marks  have  failed 
to  take  account  of  the  sexes  of  the  pupils  involved.  With  the  onset 
of  adolescence,  and  even  before,  sex  differences  become  so  marked 
that  there  would  seem  to  be  no  excuse  for  this  neglect.  It  may  be 
advanced  as  a  general  principle  that  the  sex  factor  should  be 
considered  in  every  study  dealing  with  school  marks,  no  matter 
what  the  ages  of  the  pupils,  unless  there  is  preliminary  evidence 
to  show  that  it  is  of  no  importance.  We  have  no  mere  ''pupils''  in 
our  schools ;  each  is  either  male  or  female. 

5.  Some  studies  have  been  based  upon  typical  marks  only, 
rather  than  upon  all  of  the  marks  earned  by  the  pupils  concerned. 
Among  these  typical  marks  are  failures,  promotions,  and  honors. 
Where  such  marks  are  sufficient  to  answer  the  questions  raised,  their 
use  is  a  means  of  great  simplification,  but  it  is  doubtful  whether 
in  general  they  are  completely  satisfactory  indices  of  a  pupil's 
work. 

6.  When  the  foregoing  questions  have  been  disposed  of,  it 


'Jones,  A.  L.     Entrance  examinations  and  college  records.     Educational 
Review,  Vol.  48,  109-122. 


METHODS  PURSUED  IN  EARLIER  STUDIES  17 

usually  becomes  necessary  to  reduce  the  marks  to  comparable 
numerical  form.  Here  the  procedure  described  in  Step  1  of  Section 
1  may  be  followed,  or,  as  is  more  common,  the  units  of  a  letter  scale 
may  be  given  values  other  than  percentage  equivalents."^  It  should 
be  repeated  that  in  studies  of  continuity  we  are  concerned  with 
comparing  two  series  of  marks  earned  by  the  same  group  of  students. 
Thus,  it  is  clear  that  while  the  marks  in  each  series  should  be  re- 
duced to  the  same  terms,  it  is  not  necessary  that  both  series  be 
alike  if  the  ranking  method  of  comparison  (see  Step  7a)  be  adopted.^ 

We  now  come  to  a  parting  of  the  ways.  Two  general  methods 
for  ascertaining  the  degree  of  continuity  between  the  two  series  now 
present  themselves.  One  is  by  comparison  of  absolute  marks;  the 
other  is  by  means  of  relative  ranks.  Methods  differ  radically  in 
the  two  cases. 

7.  Step  7  is  the  final  step  in  determining  degree  of  continuity 
if  one  follows  the  method  of  comparing  the  totals  of  absolute  marks. 
Three  forms  of  this  method  appear  in  the  studies  reviewed. 

(a).  Morgan^  comments  upon  the  value  of  "conditional  pro- 
motions ' '  in  the  University  of  Chicago  High  School,  by  comparing 
the  total  percents  earned  by  a  group  of  conditioned  pupils  during 
a  given  term,  with  the  total  percents  earned  by  the  same  group 
during  the  term  following  their  conditioned  promotion. 

(b) .  Grayi^  compares  the  efficiency  of  pupils  in  certain  school 
subjects  from  year  to  year  by  finding  the  differences  between  the 
percentage  marks  received  by  each  pupil  each  year,  and  then  totaling 
and  averaging  these  differences. 


'Here  the  greatest  variety  prevails.  One  approach  to  a  scientific  method  for 
finding  substitutional  values  has  been  worked  out  by  Burris,  W.  P.  Correla- 
tions of  abilities  involved  in  secondary  school  work.  Columbia  University  Con- 
tributions to  Philosophy,  Psychology  and  Education,  Vol.  9,  No.  2,  pp.  16-28. 
For  the  best  work  of  this  sort  to  date,  see  Kelley,  T.  L.  Educational  Guidance. 
Columbia  University  Contributions  to  Education.     No.  71,  pp.  86-92. 

*To  illustrate  the  comparison  of  twQ  ranked  series  which  are  based  respec- 
tively upon  two  entirely  different  marking  systems,  see  Thorndike,  E.  L.  An 
empirical  study  of  college-entrance  examinations.  Science,  N.  S.,  Vol.  23, 
839-845. 

"Morgan,  W.  P.  Conditional  promotions  in  the  University  High  School. 
School  Review,  Vol.  19,  238-247. 

^"Gray,  C.  T.  Variations  in  the  Grades  of  High-School  Pupils.  Educational 
Psyschology  Monographs.    No.  8,  Baltimore,  1913. 


18  THE  SIXTEENTH  YEARBOOK 

8.  Step  8  completely  displaces  Step  7  in  studies  of  another 
character,  which  seek  to  determine  continuity  by  means  of  ranks 
rather  than  by  absolute  marks.  Here  the  students  are  ranked  ac- 
cording to  the  scholarship  merit  displayed  individually  in  each  of 
two  subjects  or  stages,  with  or  without  reducing  the  marks  to  com- 
parable bases  as  described  in  Step  3.  Where  the  ranking  is  based 
directly  upon  the  marks  of  individual  teachers  or  individual  schools, 
this  reduction  is  unnecessary,  and  Step  8  replaces  Step  3  also.  The 
following  modes  of  ranking  appear  in  the  studies  reviewed : 

(a).  Ranking  according  to  marks  received  in  each  separate 
recitation  group  under  the  same  teacher.  This  method  is  un- 
doubtedly the  best  in  most  cases  where  the  original  marks  are  in 
the  form  of  percents,  as  it  avoids  errors  arising  from  combining 
the  marks  given  by  different  teachers.  ^^  Where  the  letter  scale  is 
used,  however,  and  where  only  one  mark  appears  for  each  pupil, 
too  many  pupils  must  ordinarily  be  assigned  the  same  rank.  This 
is  particularly  disastrous  when  the  tertile,  quartile,  or  quintile 
grouping  is  to  follow.  In  such  a  case,  actual  trial  has  shown  that 
more  than  three-fourths  of  the  students  will  be  assigned  to  their 
quartile,  or  quintile  positions  largely  by  chance. 

(b) .  Ranking  based  upon  accumulated  marks.  Here  all  of  the 
marks  given  to  a  pupil  by  different  teachers  are  brought  together 
before  the  ranking  takes  place.  Ranks  may  then  be  based  upon  (1) 
a  comparison  of  the  total  values  of  the  percents  or  letter-equival- 
ents,^ 2  Qj.  (2)  a  comparison  of  their  average  values.  The  latter 
method  is  by  far  the  more  common  one. 

Where  pupils  from  two  or  more  elementary  schools  have  been 
studied  for  their  high-school  continuity  in  scholar  ship  rank,  or 
pupils  from  two  or  more  high  schools  for  college  continuity,  in  most 
cases  (1)  the  students  have  been  ranked  in  each  school  separately, 
but  in  some  cases  (2)  all  of  the  students  have  been  thrown  together 
before  the  ranking  has  been  made,  irrespective  of  differences  in  the 
marking  standards  prevailing  in  the  different  schools.^  ^  It  seems 


"Gray,  C.  T.:  op.  cit.  See  also  Starch,  D.  Correlations  among  abilities  in 
school  subjects.    Journal  of  Educational  Psychology,  Vol.  4,  415-418. 

"Thorndike,  E.  L.,  op.  cit. 

"See  Shallies,  G.  W.  Distribution  of  high-school  graduates  after  leaving 
school.    School  Beview,  Vol.  21,  81-91. 


METHODS  PUBSUED  IN  EARLIER  STUDIES  19 

needless  to  say  that  only  the  former  of  these  last  two  methods  is 
permissible. 

The  weakness  of  the  method  of  ranking  according  to  accumu- 
lated marks  is  that  it  assumes  that  a  mark  given  by  one  teacher  is 
equivalent  to  a  mark  of  the  same  denomination  given  by  any  other 
teacher.  This  assumption  is  not  valid.  Some  teachers  consistently 
mark  much  higher  than  others,  so  that  the  70  of  one  teacher  may 
be  as  good  as  the  85  of  another.  However,  where  the  study  in- 
volves enough  cases  these  errors  will  possibly  balance  each  other. 
But  in  a  study  involving  a  few  cases  the  method  described  in  the 
preceding  section  should  be  adopted,  and  the  marks  of  the  differeni 
teachers  should  be  so  weighted  as  to  be  made  comparable. 

9.  When  a  group  of  students  has  been  ranked  in  order  of 
merit  from  poorest  to  best  according  to  the  quality  of  work  done 
by  them  at  one  stage  of  their  course  or  in  one  school  subject,  and 
has  also  been  ranked  according  to  the  efficiency  shown  at  another 
stage  or  in  another  subject,  the  type  of  study  with  which  we  are 
now  dealing  seeks  to  determine  the  degree  of  continuity  obtaining 
between  these  two  rankings.  Does  a  student  who  ranks  high  in  the 
first  series  also  rank  high  in  the  second  series,  and  vice  versa  ?  The 
following  methods  have  been  pursued  in  attempting  to  answer  this 
question : 

(a).  The  plus  (  +  )  and  minus  ( — )  median  method.^*  In  this 
method  the  investigator  finds  the  number  of  those  ranking  above  or 
below  the  median  in  the  first  series,  who  continue  to  rank  above  or 
below  the  median  in  the  second  series. 

(b).  The  modified-median^ ^  or  tertile-median^^  method.  Here 
the  investigator  finds  the  proportion  of  those  students  ranking  in 
the  highest  tertile  in  the  first  series  who  rank  above  the  median  in 
the  second  series.  The  continuity  between  the  lowest  third  and 
lower  half  is  similarly  ascertained. 

(c).     Coefficients  of  correlation.     The  coefficients  which  have 


"Dearborn,  W.  F.  Qualitative  elimination  from  school.  Elementary  School 
Teaclier,  Vol.  10,  1-13. 

"Clement,  J.  A  Standardization  of  the  Schools  of  Kansas.  University  of 
Chicago  Press,  1912. 

"Dearborn,  W.  F.  Practical  results  of  recent  studies  in  educational  statis- 
tics.    School  Rc'view,  Vol.  21,  297-306. 


20  TRE  SIXTEENTH  YEAEBOOK 

been  chiefly  used  for  the  determination  of  positional  continuity  are 
the  Pearson  ''product-moments''  and  the  Spearman  ''rank-dif- 
ference" methods.  It  is  not  our  purpose  in  this  connection  to 
describe  and  explain  in  full  these  methods.  They  are  implements 
of  general  statistics,  which  have  been  borrowed  from  that  larger 
field  by  educational  statisticians,  and  have  been  described  already 
in  many  places.^  "^ 

However,  the  writer  is  persuaded  that  there  has  existed  a 
tendency  to  resort  to  these  highly  specialized  measures  when  simpler 
measures  would  better  serve  the  purpose.  Where  a  simple  quanti- 
tative statement  of  the  probable  general  relationship  existing  be- 
tween two  series  of  variables  is  all  that  is  demanded,  the  correla- 
tion coefficients  will  often  serve  admirably.  But  where  more  than 
this  is  wanted  they  are  useless,  for  they  can  give  no  more.  They  do 
not  generally  indicate  relations  obtaining  between  particular 
portions  of  the  two  series  of  variables,  nor  do  they  reveal  the  peculi- 
arities of  form  which  either  series  may  possess.  In  a  field  of 
research  so  immediately  practical  as  educational  research  may  and 
should  be,  these  relations  and  forms  are  often  more  important  than 
the  general  relations,  so  that  the  inadequacy  mentioned  becomes 
serious. 

(d).  Method  gf  tertile,  quartile,  or  quintile  continuity.  In 
this  method  each  of  the  two  ranked  series  is  divided  into  three,  four 
or  five  equal  numerical  parts  by  beginning  at  the  upper  end  of 
each  series  and  counting  downward.  The  students  occupying  each 
position  in  the  first  series  are  then  traced  to  their  respective  posi- 
tions in  the  second  series,  and  their  positional  continuity  determined. 
Various  methods  of  stating  this  continuity  have  been  devised. 

(1).  Simple  statement  of  the  percentages  of  the  students  oc- 
cupying the  low,  middle,  and  high  groups  in  the  first  series  who 
are  found  in  each  group  in  the  second  series.^^ 


"Whipple,  G.  M.     Manual  of  Physical  and  Mental  Tests.     Warwick  and 
York,  Second  Edition,  1915,  Part  I. 
^'Clement,  J.  A.    Op.  cit. 


METHODS  PUBSUED  IN  EABLIEB  STUDIES  21 

( 2 ) .  Method  of  ' '  gains  and  losses.  ^ '  This  method  was  devised 
by  Gray,  and  corresponds  to  the  same  author 's  method  of  gains  and 
losses  in  the  use  of  percentage  marks  described  above.  It  consists 
in  finding  the  algebraic  sum  of  the  quintile  variations  undergone  by 
the  different  pupils  in  passing  upward  from  grade  to  grade.  The 
same  principle  is  applicable  in  estimating  the  amount  of  tertile  or 
quartile  variation.  It  was  applied  to  the  study  of  tertile  variation 
in  the  recent  Cleveland  survey. 

(3).  Graphic  representation-  Different  forms  of  graphic  rep- 
resentation have  been  proposed  by  Clement^^  and  Carter. 20  As 
both  of  these  sources  are  readily  accessible,  it  seems  unnecessary  to 
reproduce  their  methods  here. 

(e).  Kelly 21  has  pointed  out  a  rather  obvious  defect  of  the 
tertile,  quartile,  or  quintile  method  of  correlation,  and  has  proposed 
a  means  of  avoiding  this  defect  which  can  be  applied  to  continuity 
studies.  The  defect  is  described  thus :  '  *  When  a  distribution,  say 
of  fifty  marks,  is  divided  into  quintiles,  the  tenth  mark  needs  to 
change  but  one  rank  in  order  to  fall  into  the  next  quintile,  and 
thus  register  one  quintile  change.  The  first  individual  in  the  dis- 
tribution, on  the  other  hand,  has  to  change  by  as  much  as  ten  ranks 
in  order  to  register  one  quintile  change. ' ' 

He  describes  his  means  of  avoiding  the  defect  as  follows : 

"If  we  record  in  the  left-hand  column  of  the  accompanying  table  the 
ranks  of  the  boys  in  their  own  high-school  group,  and  in  the  second  column 
their  ranking  in  the  freshman  college  group,  we  may  count  the  quintile  gains 
or  losses  by  subtracting  each  rank  from  the  corresponding  rank  in  the  other 
series.  If  this  difference  equals  one-fifth  of  the  total  number  of  ranks  in  the 
series,  it  will  register  as  one  quintile  change.  If  it  equals  two  fifths  of  the 
number  of  ranks  in  the  series  it  will  register  as  two  quintile  changes,  etc.  For 
example,  in  the  table  given  herewith,  from  fourth  to  eighteenth  rank  is  a  change 
of  fourteen  places  and  we  register  a  loss  of  one  quintile.  From  tenth  to  forty- 
ninth  place  is  a  drop  of  three  quintiles,  etc. ' ' 


"See  Clement,  J.  A.    Op.  cit. 

'"Carter,  R.  E.    Correlation  of  elementary  and  Tiigh  schools.     Elementary 
School  Teacher,  Vol.  12,  109-118. 

-^Kelly,  F.  J.    Teachers '  Maries.    Teachers '  College  Contributions  to  Edue. 


22  THE  SIXTEENTH  YEAEBOOK 


KELLY'S  TABLE. 

HIGH-SOHOOL 

FRESHMAN    COLLEGE 

QUINTILE  GAINS 

RANKS. 

RANKS. 

OR    LOSSES. 

1 

3 

0 

2 

5 

0 

3 

2 

0 

4 

18 

—1 

5 

8 

0 

6 

19 

—1 

7 

7 

0 

8 

14 

0 

9 

9 

0 

10 

49 

—3 

11 

17 

0 

12 

6 

0 

42 

38 

0 

43 

13 

3 

44 

22 

2 

45 

25 

2 

46 

21 

0 

47 

42 

0 

48 

23 

2 

49 

34 

1 

50 

48 

0 

The  point  which  Kelly  makes  is  undeniably  valid,  and  the  sub- 
stitute method  is  useful  in  certain  types  of  continuity  studies.  But 
in  the  present  writer 's  opinion  Kelly  has  over-stressed  both  the  im- 
portance of  his  criticism  and  the  value  of  his  substitute  method. 
The  criticism  which  he  advances  may  be  made  with  equal  propriety 
upon  every  marking  system  now  in  use,  in  that  all  of  them  involve 
a  series  of  discrete  units.  That  is  to  say,  the  different  units  in  any 
marking  system,  however  numerous,  are  sharply  separated  each 
from  each,  like  steps  in  a  stair,  while  the  variations  in  scholarship 
represented  by  these  marks  are  continuous,  and  in  a  large  group 
ranked  in  serial  order  may  be  practically  infinitesimal.  Some  stu- 
dents are  clearly  A  students ;  others  are  less  clearly  A  students ;  yet 
both  will  be  marked  A.  The  only  marking  system  which  even  nom- 
inally avoids  this  difficulty  is  the  percentile  system,  because  of  its 
more  numerous  and  consequently  finer  discriminations:  yet  it  is 
very  doubtful  whether  these  finer  distinctions  are  anything  more 
than  artificial.  Furthermore,  the  final  step  in  Kelly's  method  also 
involves  a  discrete  series,  and  introduces  again  the  very  type  of 
error  that  it  is  designed  to  avoid.    Finally,  it  is  a  method  that  can- 


METHODS  PUBSUED  IN  EABLIEB  STUDIES  23 

not  be  applied  in  any  way  to  studies  of  comparison,  because  in  these 
studies  the  different  ranked  series  comprise  different  groups  of  stu- 
dents. 

In  the  methods  which  we  have  described  we  have  noted  the  divi- 
sion of  the  ranked  series  into  halves,  tertiles,  quartiles,  and  quin- 
tiles.  There  is  evidence  of  a  growing  preference  for  the  tertile  or 
quintile  divisions,  because  an  even  division  into  either  halves  or 
quartiles  splits  the  mediocre  group  in  two,  while  the  odd  divisions 
leave  this  middle  group  intact  and  differentiate  those  students  who 
rise  above  or  fall  below  mediocrity.  Of  the  two  odd  divisions  the 
quintile  is  increasing  in  use,  probably  because  of  the  finer  distinc- 
tions of  which  the  more  numerous  divisions  permit. 

Section  3 
studies  of  comparison 

Definition.  Under  the  head  of  comparative  studies  we  include 
those  whose  principal  aim  has  been  to  compare  the  attainments  of 
different  groups  of  pupils  as  evidenced  by  their  school  marks.  The 
significant  feature  here  is  the  comparison  of  the  records  of  one 
group  of  students  with  those  of  another  group,  rather  than  to  com- 
pare the  same  group 's  records  made  under  different  circumstances, 
as  in  the  continuity  studies.  No  uniform  methodology  has  been 
worked  out  for  studies  of  comparison,  and  considerable  variation 
appears  in  consequence.  The  following  paragraphs  record  only  the 
most  common  methods. 

MetJiods.  Steps  1  to  6  in  methods  of  comparison  may  be  bor- 
rowed directly  from  the  corresponding  steps  described  under  meth- 
ods of  continuity. 

7.  Comparisons  may  be  based  directly  upon  accumulated 
marks.  Where  this  method  is  used,  it  is  necessary  to  put  into  com- 
parable form  marks  earned  by  each  of  the  groups  of  students  whose 
efficiency  is  to  be  compared.  For  this  purpose  one  may  adopt  any 
of  the  following  devices : 

(a)  Total  the  marks  of  each  denomination,  or  their  numerical 
equivalents.  That  is  to  say,  bring  together  all  of  the  A 's,  B  *s,  or 
other  marks  earned  by  each  group  of  students  to  be  compared.  Here, 
again,  one  encounters  the  problem  of  the  different  marking  stand- 


24  TEE  SIXTEENTH  TEABBOOK 

ards  held  by  different  teachers,  and  the  warnings  given  above  must 
be  respected. 

(b)  If  the  differences  between  the  groups  that  are  to  be  com- 
pared are  pronounced,  and  if  no  precise  statement  of  the  amount 
of  these  differences  is  desired,  one  may  next  simply  plot  curves  to 
show  the  distribution  of  marks  in  each  of  the  student  groups.22 
Directions  for  plotting  these  curves  have  already  been  given  in  Step 
3  of  Section  1. 

(c)  If,  however,  the  investigator  wishes  to  make  a  precise 
statement  of  the  amounts  of  the  differences  obtaining  between  the 
various  student  groups,  another  method  must  be  adopted.  Here 
may  be  used  any  of  the  established  statistical  modes  of  stating  cen- 
tral tendencies  and  variations.  These  methods  have  already  been 
described  and  discussed  too  widely  to  need  extensive  treatment  in 
this  place. 

(8) .  Step  8  should  be  entirely  substituted  for  Step  7  when  the 
ranking  plan  is  to  be  used  for  purposes  of  comparison.  This  plan 
should  generally  be  substituted  for  the  simpler  one  based  upon 
absolute  marks,  when  schools  with  different  marking  systems  are 
involved  in  the  same  study.  The  methods  to  be  pursued  in  the  rank- 
ing process  are  similar  to  those  described  in  Step  8  of  Section  2.  It 
has  been  customary  to  follow  this  ranking  by  a  division  of  each 
ranked  series  into  tertiles,  for  each  comparative  group  and  in  each 
school,  as  in  the  studies  of  continuity. ^^  The  tertile  positions  of  the 
different  members  of  each  comparative  group  many  then  be  assem- 
bled, and  rough  comparisons  made  upon  the  basis  of  these  totals. 
No  precise  method  for  stating  this  comparison  has  yet  been  devised. 


^Johnson,  F.  W.  A  study  of  high-school  grades.  School  Beview,  Vol.  19, 
13-24. 

23See  Shallies,  G.  W.  Op.  cit. ;  Mitchell,  H.  E.  Distribution  of  high-school 
graduates  in  Iowa.  School  Beview,  Vol.  22,  82-91.  Pittenger,  B.  F.  Distribu- 
tion of  hiffh-sehool  graduates  in  five  North  Central  states.  School  and  Society, 
Vol.  3,  901-907. 


II 


CHAPTER  II 

RESULTS  OF  EARLIER  STUDIES  CONCERNED  WITH  AGE 
AT  ENTRANCE  AND  WITH  SIZE  OF  HIGH  SCHOOL 

In  the  foregoing  chapter  the  writer  has  attempted  to  arrange 
and  criticize  the  various  methods  used  in  earlier  studies  dealing  with 
school  and  college  marks.  Such  a  critique  is  necessary,  since  we 
propose  to  utilize  similar  materials.  But  there  is  another  group 
of  studies  which  demands  consideration  here  because,  while  based 
upon  different  materials,  it  is  directed  toward  problems  similar  to 
those  raised  in  this  investigation.  However,  it  is  the  results  and 
not  the  methods  of  these  studies  which  are  of  interest  at  this  point. 

Section  1 
studies  concerned  with  age  at  entrance  into  the  elementary 

SCHOOL 

One  of  the  first  books  bearing  even  indirectly  upon  this  ques- 
tion was  published  by  C.  H.  Keyes^  in  1911.  Keyes  studied  the 
influence  of  several  different  factors,  one  of  which  was  age  at  en- 
trance, upon  the  rate  and  consistency  of  progress  through  the 
grades.  The  question  of  efficiency  as  displayed  by  marks  or  other 
qualitative  symbols  was  not  raised.  The  influence  exerted  by  age 
at  entrance  upon  grade  progress  is  shown  in  the  following  quota- 
tions : 

"Practically  all  children  who  begin  the  first  grade  after  reaching  their 
seventh  birthday,  or  before  reaching  their  fifth,  may  be  expected  to  lose  a  year 
during  some  part  of  their  grammar-school  course." 

'  *  Of  all  who  enter  the  first  grade  under  five  years  of  age  only  one  in  nine 
gains  a  grade  during  the  course.  Of  those  who  enter  during  their  fifth  year, 
one  in  four  makes  such  a  gain;  while  more  than  one  in  every  three  who  enter 
after  reaching  their  sixth  birthday  gain  a  year  at  some  time  during  the  course. ' ' 
But  *  *  this  does  not  mean  that  there  is  no  gain  in  starting  children  to  school  at 
an  early  age  if  they  are  psychologically  fit, '  ^  inasmuch  as  "60  percent  of  the 
early  entrants  preserve  the  advantage  of  the  year  over  the  average  child. ' '  The 
loss  found  among  the  early  entrants  is  thus  assumed  to  be  due  to  the  presence 
of  undeveloped!  children. 


^Keyes,  C.  H.    Progress  through  the  Grades  of  City  Schools.    Teachers  Col- 
lege Contributions  to  Education.     No.  42.     N.  Y.,  1911. 

25 


26  THE  SIXTEENTH  YEABBOOK 

'*  Arrest  is  most  likely  to  follow  too  early  or  too  late  entrance  to  school. 
Fifty  percent  of  all  children  who  enter  grade  one  before  the  age  of  five  years 
meet  arrest  at  some  place  in  the  course;  likewise  46  percent  of  those  entering 
between  seven  and  seven  and  one-half  years,  and  49  percent  of  all  entrants  over 
seven  and  one-half  years,  become  arrests." 

The  general  outcome  of  this  investigation  is  to  establish  six  and 
seven  as  the  best  ages  for  entrance  into  elementary  school,  with 
distinct  preference  for  the  age  of  six. 

The  second  investigation  of  this  character^  was  published  by 
W.  H.  Winch,  in  1911.  Winch's  study  was  conducted  in  the  ele- 
mentary schools  of  England  where  entrance  conditions  are  very  dif- 
ferent from  those  in  America ;  but,  because  it  deals  with  earlier  ages 
than  are  comprised  in  the  American  studies,  it  may  be  reviewed 
with  some  care. 

In  England,  children  may  enter  school  at  three  years  of  age,  and 
must  enter  at  five.  While  some  enter  a  few  months  after  five,  the 
great  majority  of  entries  are  distributed  indiscriminately  between 
these  ages.  Winch  sought  to  discover  the  correlation  between  dif- 
ferent portions  of  this  two-year  entrance  period,  and  school 
efficiency. 

Two  measures  of  school  efficiency  were  adopted ;  one  called  the 
* '  progress  mark, ' '  and  the  other  a  scholarship  mark  based  upon  the 
Head-Master's  examinations  in  the  later  *' Standards"  (grades). 
The  second  of  these  criteria  is  easily  comprehended,  but  the  first 
requires  some  explanation.  The  grades  of  the  English  elementary 
school  range  from  Standard  I  to  Standard  VII,  being  preceded  gen- 
erally by  a  short  term  in  the  infant  school.  It  is  age  of  entrance  in 
the  infant  school  with  which  Winch  is  concerned.  The  accepted 
age  for  beginning  Standard  I  is  6  years  and  6  months,  and  for  be- 
ginning Standard  VII  is  12  years  and  6  months.  Many  students  are 
two  years  behind  this  program  in  the  latter  end  of  this  course,  and 
but  few  are  slower  than  that;  ''so,"  says  Winch,  ''I  took  the  pupil 
who  was  two  years  behind  as  being  credited  with  0  progress  marks, 
and  those  who  were  more  than  two  years  behind  received  a  negative 
mark.  The  ages  of  the  children  were  calculated  in  months,  so  that 
a  boy  two  years  and  one  month  behind  would  receive  a  negative 
mark  of  one.    If  he  were  one  year  and  eleven  months  behind  he 


^'Winch,  W.  H.    When  Should  a  Child  Enter  School?    Baltimore,  1911. 


BESULTS  OF  EABLIEB  STUDIES 


27 


would,  of  course,  receive  a  positive  mark  of  one ;  if  he  were  just  right 
his  mark  would  be  24 ;  and  if  he  were  one  year  ahead  of  the  normal 
age  ....  he  would  receive  a  positive  mark  of  36. '^  Hence  **we 
have  merely  to  take  the  age  in  years  and  months  when  he  entered  his 
present  standard,  and  add  to,  or  subtract  from  24,  the  months  by 
which  he  is  in  advance  of,  or  behind  the  normal  age"  (pp.  10-11). 
''If  now  we  collect  the  progress  marks  of  all  children  who 
entered  between  3  and  3i/^  years  of  age,  and  of  all  those  who  entered 
between  3i/^  and  4  years,  and  so  on,  we  ought  to  see  at  a  glance 
whether  there  is  any  marked  correlation  between  age  of  entry  and 
subsequent  progress  in  school."  Two  sample  tables  from  Winches 
results  are  given  herewith. 

SCHOOL  ''G^'— BOYS 


Age  of 
Entry 


Number 
Pupils 


Av.  Prog.  Mark 
per  Pupil 


3-3  Va 

12 

3y2-4 

7 

4-4y2 

8 

m-5 

16 

5-5  Va 

12 

sva-e 

2 

3-3^2 

7 

3y2-4 

4 

4-4  Va 

15 

41/2-5 

10 

5-5  Va 

25 

5y2-6 

Av.  Exam. 

Mark 
(Max.  10) 


Pearson 

Coefficient 

(Age  with  Prog.) 


Probable 
Error 


20.6 

7.5 

19.4 

7.2 

21.6 

7.9 

19.0 

7.9 

15.4 

7.7 

17.0 

•• 

SCHOOL 

"G"— GIELS 

19.0 

7.9 

20.7 

8.2 

20.8 

7.0 

20.5 

7.8 

19.3 

8.2 

-.1727 


.09 


-.0116 


.08 


Tables  corresponding  to  these  two,  and  displaying  very  similar 

tendencies,  are  presented  for  eight  boys'  schools  and  three  girls' 

schools,  after  which  the  author  writes : 

*'I  think  we  may  fairly  conclude  that,  so  far  as  intellectual  results  are 
concerned,  and  in  so  far  as  these  are  measured  by  school  progress,  we  can  claim 
no  advantage  for  early  entry  into  school;  that  is,  children  who  enter  at  three 
years  of  age  progress  neither  more  rapidly  nor  more  decisively  than  those  who 
enter  at  five.  I  do  not  consider  that  the  evidence  is  satisfactory  for  entrance 
ages  beyond  five  years,  as  the  numbers  are  small.  ...  I  conclude,  however, 
with  confidence  that,  as  far  as  subsequent  school  progress  is  concerned,  it  is 
of  trifling  importance,  if  not  absolutely  unimportant,  whether  a  child  begins 
school  at  three  or  at  five  years  of  age"  (p.  38). 


28  THE  SIXTEENTH  YEABBOOK 

The  other  significant  conclusions  reached  after  an  elaborate  an- 
alysis, are : 

(1)  ^'That  children  who  come  from  very  poor  homes,  that  is,  from  homes 
in  which  there  is  no  adequate  supervision  for  the  young  child,  are  smaller  in 
number  than  is  generally  supposed ;  and  that  even  under  present  conditions,  such 
children  commence  to  attend  school  not  at  one  special  age,  but  fairly  evenly, 
in  the  same  proportions  as  other  children,  between  the  ages  of  three  to  five  and 
one-half  years.  But  not  quite  evenly:  there  is  some  positive  correlation  be- 
tween poor  homes  and  early  entry."  (2)  '*No  advantage  appears  to  exist  in 
early  entry  so  far  as  the  subsequent  attainment  of  good  behavior  and  the 
development  of  attentiveness  are  concerned. ' ' 

The  conclusions  of  this  rather  extensive  and  elaborate  investi- 
gation: are  thus  chiefly  negative  in  character :  the  chief  point  of  a 
positive  nature  is  that  children  who  enter  school  much  before  five 
afterward  lose  sufficient  time  so  that  they  arrive  at  the  end  of  their 
course  at  practically  the  same  age  as  the  five-year-old  entrants. 

The  third  paper  of  the  series  now  under  discussion  was  brought 
out  by  Ayres,^  in  1912.  Three  separate  studies  are  combined  in 
this  report,  from  which  we  will  quote  what  bears  on  our  problem. 

' '  In  1908,  the  writer  conducted  an  investigation  for  the  Board  of  Education 
of  New  York  City,  in  which  a  study  was  made  of  ...  a  group  of  257  pupils 
in  the  eight  grades,  who  were  about  to  graduate,  and  whose  entire  school  histories 
from  the  date  of  first  entering  were  intact  and  available.  The  number  of 
children  in  each  entering  age-group  and  the  time  taken  to  complete  the  course 
were  as  follows: — 

Age  at  Entrance  Number  of  Children       Av.  Years  to  Complete 

Eight  Grades 

5 64 8.9 

6 113 8i6 

7 54 8.4 

8 19 8.2 

9 7 7.2 

^'The  figures  show  a  steady  but  slight  falling  off  in  the  amount  of  time 
required  by  the  children  of  each  advancing  age-group  to  complete  the  course. 
This  decrease  is  so  small  that  it  lends  no  support  whatever  to  the  prevalent 
opinion  that  the  child  entering  school  late  will  make  such  rapid  progress  as 
easily  to  catch  up  with  the  children  who  entered  two  or  three  years  earlier. ' ' 

The  second  of  Ay  res'  studies  was  also  made  with  New  York 
City  children,  comprising  11,185  cases,  in  1909.  The  tabulated 
data  for  these  children  follow : 


'Ayres,  L.  P.  The  Belation  Between  Entering  Age  and  Subsequent  Progress 
Among  School  Children.  Bulletin  No.  112,  Division  of  Education,  Russell  Sage 
Foundation,  1912. 


BESULTS  OF  EARLIER  STUDIES  29 

Age  at  Entrance  Number  of  Children      Median  Years  to  Complete 

Eight  Grades 

5 1521 8.2 

6 5828 8.1 

7 2936 8.0 

8 721 7.9 

9 142 7.4 

10 26 6.9 

11 9 6.6 

12 2 6.3 

*' These  figures  again  expose  the  fallacy  of  the  common  assertion  that  the 
child  entering  late  easily  catches  up  with  the  one  who  begins  early. ' ' 

The  third  set  of  data  is  still  more  significant.  This  material 
was  collected  through  the  Division  of  Education  of  the  Russell  Sage 
Foundation,  and  comprised  13,867  cases,  from  the  schools  of  29 
cities.    The  tabulated  data  follow : 

Age  at  Entrance  Number  of  Children      Median  Years  to  Complete 

Eight  Grades 

5 2663 8.7 

6 6050 8.5 

7 3653 8.2 

8 1151 7.8 

9 255 7.2 

10 58 6.3 

11 22 

12 9 

13 3 

14 4 

' '  These  figures  closely  resemble  the  two  foregoing  series.  They  show  that 
the  children  who  enter  school  at  advanced  ages  gain  a  little  on  those  who  enter 
early,  and  that  this  gain  becomes  greater  as  the  upper  ages  are  reached.  They 
again  show  that  this  gain  is  not  enough  to  enable  the  late  entering  child  to 
catch  up  with  the  one  who  enters  early. ' ' 

After  this  discussion,  the  author  proceeds  to  select  the  most 
auspicious  entrance  age.  With  the  group  of  records  from  the  29 
cities,  '*a  division  into  three  progress  groups  was  made  in  which 
those  pupils  who  had  taken  more  than  eight  years  to  complete  the 
eight  grades  were  designated  as  slow,  those  who  had  taken  just 
eight  years  as  normal,  and  those  getting  through  in  less  than  eight 
years  were  termed  rapid.  The  children  of  each  entering  age  were 
divided  among  these  three  progress  groups  as  follows : 


gQ  TEE  SIXTEENTH  YEARBOOK 


Age  at 
Entrance 

5     

Percent 
Eapid 
10 

Percent 
Normal 

, 58   

52   

Percent 
Slow 
32 

fi 

27 

40 

59 

81 

21 

7 

8 

9       

, 45   

33 

, 17   

15 

8 

2 

10 

98 

100 

2   

11 

12 

100 

13 

100   

14 

100 

*  *  Is  the  best  entering  age  the  one  which  results  in  the  greatest  proportion 
of  rapid  pupils,  the  smallest  proportion  of  slow  pupils,  the  largest  proportion 
of  normal  pupils,  or  the  most  equal  balance  between  these  three  groups?  The 
writer  is  inclined  to  the  opinion  that  .  .  .  the  best  entering  age  is  the  one  that 
results  in  a  large  proportion  of  normal  pupils,  combined  with  the  most  equal 
balance  between  the  rapid  and  slow  groups.  In  the  present  case  this  is  the 
entering  age  of  six. ' ' 

This  table  is  checked  by  comparison  with  another  *' which  con- 
siders a  fourteen-year-old  child  in  the  eighth  grade  as  of  normal  age, 
one  younger  as  below  normal  age,  and  one  older  as  above  normal 
age.'' 

Age  at         Percent  Percent         Percent 


itrance 

Young 

Normal 

Over-j 

5 

67   

25 

8 

6 

27   

52   

21 

7 

8   

33   

59 

8 

3   

14 

83 

9 

2   . 

7 

91 

10 

2   

10 

88 

11 ...... . 

5 

95 

12 

100 

13 

100 

14 

100 

This  table  resembles  the  preceding  ' '  in  that  the  entering  age  of 
six  is  the  one  which  results  in  combining  the  greatest  proportion 
of  normal  pupils  with  the  most  equal  balance  between  the  young 
and  over-age  groups. ' '  These  results  are  further  substantiated  by 
finding  that  the  six-year-old  entrants  graduate  most  nearly  on  nor- 
mal time,  and  that  this  group  shows  the  greatest  homogeneity  in  its 
progress  rate. 

Ayres  concludes  that,  using  rate  of  progress  through  the  grades 
as  the  criterion,  late  entrants,  while  progressing  more  rapidly  than 


EESULTS  OF  EABLIEB  STUDIES  31 

early  entrants,  do  not  generally  overtake  them;  and  that  ''the  en- 
trance age  of  six  is  the  one  which  makes  the  best  showing  with  re- 
spect to  resulting  in  the  largest  number  of  the  children  finishing  the 
course  at  normal  age,"  and  with  respect  to  furnishing  "the  most 
homogeneous  group,  judged  on  the  basis  of  subsequent  progress." 

Section  2 

studies  concerned  with  age  at  entrance  into  the  high  school 

In  a  little  volume  entitled  TJie  Higli  School  Age,  Irving  King'* 
devotes  a  chapter  to  the  further  elaboration  of  earlier  studies  made 
by  Van  Denburg^  and  Dynes,^  in  so  far  as  they  dealt  with  age  at 
entrance.  He  seeks  first  to  ' '  gain  some  idea  of  the  probable  ability, 
at  the  time  of  entering  high  school,  of  high-school  boys  and  girls 
as  compared  with  school  children  in  general. ' '  The  median  age  of 
high-school  entrance  as  found  by  Dynes  was  14.9,  by  Van  Denburg 
14.5;  "that  is,  one-half  of  all  the  pupils  studied  in  these  two  cities 
(Iowa  City  and  New  York)  entered  before  fifteen-"  "In  Iowa  City 
the  children  entering  the  elementary  school  probably  average  six 
years  of  age.  In  New  York  City  the  average  age  of  entrance  is 
given  as  seven.  If  these  Iowa  City  children  are  regularly  promoted 
they  finish  the  elementary  course  in  eight  years,  or  at  the  end  of  the 
fourteenth  year.  Similarly,  New  York  City  children  would  nor- 
mally finish  the  elementary  schools  at  the  end  of  the  fifteenth  year. 
If,  then,  more  than  half  of  those  entering  the  high  school  enter 
earlier  than  the  above  ages,  they  have  at  one  or  more  points  in  their 
elementary  school  work  skipped  grades  or  gained  special  promotions. 
Every  such  incident  in  the  life  of  a  child  is  an  indication  that  he  has 
possessed,  at  one  time  or  another,  more  than  average  ability  .... 
Then,  while  about  one  in  every  twenty-tJiree  of  elementary-school 
children  gain  special  promotions,  one  in  three  of  those  who  come  to 
the  high  schools  have  apparently  gained  such  promotions."  The 
natural  conclusion  is  that  high-school  entrants  are  a  highly  selected 
group.    Confirmation  of  this  inference  is  found  in  Dearborn's  in- 


*King,  Irving.  The  High  School  Age.  Bobbs  Merrill  Co.,  Indianapolis,  1914. 
''Van    Denberg,    J.    K.   The  Elimination  of  Pupils  in  Public  Secondar'^ 
Schools:    Teachers  College  Contributions  to  Education,  No.  47. 
*Dynes,  J.  J.    Study  unpublished. 


32  TEE  SIXTEENTH  YEAEBOOK 

vestigation  into  qualitative  elimination  in  the  elementary  schoolJ 
The  second  question  raised  by  King  is  as  to  the  *' relation  be- 
tween entering  age   and  the   pupil's  likelihood   of  finishing  his 
course. ' '    This  question  is  answered  in  the  form  of  a  table. 

Tahle  Showing  in  Percents  the  Comparative  Graduation  Expectancy  of  the 
Various  Entering  ages  (After  King) 


Iowa  City  New  York  City 

12-13 65 23.0 

13-14 50 19.0 

14-15 39 10.0 

15-16 29 6.5 

16-17 17 3.5 

This  table  is  followed  by  the  remark:  ''We  may  say  with  Van 
Denburg  that,  '  as  far  as  age  is  concerned,  thirteen  is  the  ideal  age 
for  high  school  entrance, '  or  even  between  twelve  and  thirteen. '  *  It 
seems  unnecessary  to  elaborate  upon  the  fallacy  of  this  remark,  in 
view  of  the  other  conclusion  just  quoted — that  high-school  pupils, 
particularly  the  early  entrants,  are  a  selected  group.  The  table 
gives  an  acceptable  indication  of  what  happens  to  those  pupils  who 
now  enter  the  high  school  at  twelve  or  thirteen ;  but  it  gives  no  indi- 
cation at  all  of  what  would  occur  if  all  pupils  were  to  enter  at  those 
ages. 

The  third  problem  raised  by  King  concerns  the  relation  between 
entering  age  and  subsequent  high-school  scholarship.  This  ques- 
tion is  answered  indirectly,  by  ascertaining  that  the  graduates,  upon 
the  whole,  do  work  which  is  very  superior  to  that  of  the  non-grad- 
uates. When  this  fact  is  coupled  with  the  earlier-mentioned  fact 
that  there  is  a  high  correlation  between  graduation  expectancy  and 
early  entrance  age,  there  is  inferred  a  similar  correlation  between 
efficiency  in  scholarship  and  early  entrance  age. 

We  may  conclude  our  summary  of  King's  discussion  with  the 
remark  that  it  seems  singularly  unfortunate  that  no  discrimination 
between  the  sexes  has  been  attempted,  during  this  period  when  sex- 
differences  might  be  expected  to  be  paramount. 

A  recent  development  in  discussions  relating  to  the  ages  of  high- 


^Dearborn,  W.  F.    Qualitative  eUmination  from  school.    Elementary  School 
Teacher,  Vol.  10,  1-13. 


BESULTS  OF  EABLIEB  STUDIES 


33 


school  (and  grammar-school)  pupils  is  to  emphasize  anatomical  or 
physiological  rather  than  chronological  age.^  *  *  The  term  anatomical 
or  physiological  age  refers  to  the  stage  of  development  in  contradis- 
tinction to  chronological  age  in  years  and  months,  which  is  our  usual 
method  of  age  designation. ' '  Various  methods  of  determining  phy- 
siological age  have  been  adopted ;  King  used  the  personal  judgments 
of  teachers  and  principals,  and  Crampton  used  the  appearance  of 
the  teeth  and  the  onset  of  puberty,  as  shown  by  menstruation  or  the 
appearance  of  pubic  hair.  In  general,  three  periods  of  development 
are  recognized;  the  pre-pubescent,  pubescent,  and  post-pubescent 
(Crampton),  or  the  immature,  the  maturing,  and  the  matured 
(King).  From  the  records  of  4,800  boys  in  New  York  City  high 
schools,  Crampton  finds  the  relations  between  anatomical  and  chron- 
ological age  shown  in  the  accompanying  table. 

Chronological  vs.  Anatomical  Age 

Chronological  Age  Anatomical  Age 

Percent  Percent  Percent 

Pre-Pubescent         Pubescent  Post-Pubescent 


12.5-13 
13-13.5 
13.5-14 

69% 

55 

41 

25% 

26 

28 

6% 
18 
31 

14-14.5 
14,5-15 
15-15.5 

26 

16 

9 

28 
24 

20 

46 
60 
70 

15.5-16 
16-16.5 
16.5-17 

5 
2 
1 

10 

4 

4 

85 
93 
95 

17-17.5 
17.5-18 

0 
0 

2 
0 

98 
100 

Regarding  the  peculiarities  of  these  developmental  periods, 
Crampton  tells  us  that ' '  at  characteristic  ages,  the  mature  are  more 


*In  connection  with  the  topic  of  physiological  age  the  reader  may  note  the 
following : 

Crampton,  C.  W.  The  Influence  of  physiological  age  upon  scholarship. 
Psychological  Clinic,  Vol.  I,  115-120. 

Crampton,  C.  W.  Anatomical  or  physiological  vs.  chronological  age.  Fed. 
Sem.,  Vol.  15,  230-237. 

Foster,  W.  L.  Physiological  age  as  a  basis  for  the  classification  of  pupils 
entering  high  school.    Fsychological  Clinic,  vol.  4,  85-88. 

King,  Irving.  Physiological  age  and  school  standing.  Fsychological  Clinic, 
Vol.  7,  222-229.    See  also  The  High  School  Age. 


34  THE  SIXTEENTH  YEARBOOK 

than  33  percent  heavier,  ten  percent  taller,  and  33  percent  stronger 
than  the  immature,"  and  that  ''the  immature  boys  of  all  ages  fail 
to  pass  the  work  of  any  grade  much  more  than  those  who  are  ma- 
ture." As  has  been  pointed  out  by  Whipple,^  this  last  statement  is 
contradicted  by  Foster,  who  found  that,  of  58  failures,  40  were  in 
the  most  mature  groups,  while,  of  179  promotions,  100  were  in  the 
least-  mature  groups.  As  Whipple  says,  more  investigation  of  this 
point  is  needed. 

King  offers  considerable  evidence  to  show  that  * '  children  of 
early  or  normal  development  in  every  case  can  do  better  work  [in 
school]  than  those  who  are  somewhat  later,  if  not  retarded,  in  their 
development. ' '  Crampton  states  that  ' '  a  preliminary  investigation 
shows  that  in  the  fifth,  sixth,  and  seventh  years  in  the  elementary 
schools  in  New  York  City,  the  poor  scholars  are  on  the  average  of 
37,  40,  and  46  percent  more  advanced  in  maturity  than  the  good 
scholars,"  but  asserts  that  *'this  is  quite  contrary  to  the  condition 
shown  in  high  schools."  The  evidence  for  the  latter  part  of  this 
statement  is  not  given,  but  the  difference  would  appear  to  be  cor- 
related with  the  retention  of  the  over-age  and  poor  pupils  in  the 
elementary  school,  and  the  promotion  of  the  brighter,  but  earlier 
maturing  pupils  into  the  high  school. 

In  practically  all  of  the  studies  quoted  above,  boys  have  been 
the  soIb  objects  of  attention,  owing  to  the  greater  difficulty  experi- 
enced in  obtaining  reliable  data  relating  to  the  pubescent  develop- 
ment of  girls.    King's  work  is  an  exception. 

The  full  bearing  of  this  matter  of  maturity  of  development 
upon  the  question  of  high-school-entrance  age  is  not  yet  clear.  One 
fact  alone  stands  out ;  i.  e.,  that  these  differences  in  maturity  are  far 
more  pronounced  and  important  during  the  freshman  year  than 
later,  when  elimination  and  increase  in  age  have  reduced  them.  It 
also  seems  probable  that  a  large  proportion  of  those  who  enter  the 
high  school  at  an  early  age  are  mature  pupils ;  and  that  the  superior 
ability  which  appears  to  be  correlated  with  this  early  maturity  is 
in  part  responsible  for  the  better  grades  and  greater  persistency  dis- 
played by  this  group.    However,  at  present  we  can  say  with  cer- 


^Whipple,  G.  M.     Psychology  and  Hygiene  of  Adolescence,  in  Monroe  ^s 
Principles  of  Secondary  Education,  Macmillan  Company,  N.  Y.,  1914.    Ch.  VII. 


RESULTS  OF  EAELIEB  STUDIES  35 

tainty  that  the  problems  affecting  high-sehool-entrance  ages  are 
closely  bound  up  with  these  problems  of  comparative  development, 
and  that  simple  chronological  age  is  a  very  inadequate  criterion  of 
readiness  to  enter  the  high  school. 

Section  3 

studies  concerned  with  age  at  entrance  into  college 

No  investigations  have  come  to  the  author's  notice  which  bear 
directly  upon  problems  of  age  and  college  entrance.  The  nearest 
approach  is  in  a  one-page  report  by  Forsyth^^  of  the  correlation 
existing  between  the  ages  of  college  students  and  their  marks.  The 
study  included  1,306  men  students  and  644  women  students  of  the 
University  of  Illinois,  for  the  school  year  1909-10.  The  men  showed 
a  Pearson  coefficient  of  0.0938,  P.  E.,  0.0685 ;  and  the  women  a  co- 
efficient of  0.1996,  P.  E.,  0.0360.  ''The  results  indicate  that,  on  the 
average,  age  has  a  little,  but  a  very  little  favorable  effect  on  schol- 
arship  Both  coefficients,  though  small,  are  well  beyond  the 

probable  error The  coefficient  for  the  women  has  more 

than  twice  the  value  of  the  one  for  the  men." 

Section  4 

studies  concerned  with  size  of  high  school 

Thorndike^^  issued  in  1907  the  first  study  dealing  with  the  size 
of  American  high  schools,  as  measured  by  number  of  teachers  em- 
ployed and  pupils  enroled.  The  data  refer  to  conditions  in  1904. 
The  tables  herewith  are  copied  or  adapted  from  this  report : 

Table  Showing  Number  and  Percentage  of  High  Schools  Employing  Different 
Numbers  of  Teachers  in  1904.  (Adapted  from  Thomdike) 

No.  Teachers  No.  Schools  Percentage  Schools 

1 2175 30 

2 1807 25 

3 1221 17 

4 640 9 

5 380... 5 


^"Forsyth,  C.  H.  Correlation  between  ages  and  grades.  Journal  of  Educa- 
tional Psychology,  Vol.  3,  164. 

"Thorndike,  E.  L.  A  Neglected  Aspect  of  the  American  High  School.  Edu- 
cational Review,  Vol.  33,  245-255.  See  also  Strayer  and  Thorndike,  Edu- 
cational Administration,  Macmillan,  1913,  165-175. 


33 


THE  SIXTEENTH  YEARBOOK 


1-5 6223, 

6 208 

7 172 

8 87 

9 74 

10 48 

5-10 588. 

11-15... 165. 

16-20 78 

21-25 63 

26-30 27 

31-35 14 

36-40 13 

41-50 9. 

51-60 8 

61-70 4 

71-80 3 

81-90 2 

91-100 0 

101-110 2 


,86 


In  schools  of 

1-3 

4-6 

7-10 

11-20 

21-30 

31-40 

41-50 

51-110 

Taile  Showing  Percentages  of  High-School  Pupils  in  Different  Sized  Schools, 
in  1904.     (After  ThorndiTce) 

1-3  teachers  are  36.6%  of  public  high-school  pupils 

,}  yy      22.1  '' 

y,  ''        9.1  '' 

''        ''     13.5  '' 

?  J  ?>  IT   IT  >  > 

J?        ''3.6  '' 

"        "2,0  '^ 

"        '^4.5  " 

Thorndike  concludes :  ' '  The  most  typical,  in  the  sense  of  the  most  frequent, 
secondary  school  in  the  United  States  is  a  school  taught  by  one  teacher.  The 
secondary  schools  in  the  country  with  only  one  teacher  outnumber  by  a  con- 
siderable figure  all  the  rest.  Those  with  one,  two,  or  three  teachers  are  ten 
times  as  frequent  as  those  with  ten  or  more  teachers  and  five  times  as  frequent 

as  those  with  from  five  up  to  ten  teachers The  frequency  of  the  schools 

of  small  teaching  force  is  so  much  greater  that  in  spite  of  the  large  registration 
of  city  high  schools  there  are  more  pupils  in  the  two-teacher  high  schools  than  in 

any  other  one  group and  more  in  schools  with  three  teachers  or  fewer 

than  in  schools  of  from  five  to  thirteen  teachers,  and  nearly,  if  not  quite,  as 
many  as  in  schools  of  fifteen  or  more  teachers.  These  facts  show  that  the  high 
school  is  ....  an  institution  of  enormous  variability  as  regards  its  capacity 
for  educational  work  and  its  administrative  and  educational  arrangements.  This 
variability  has  never  been  fully  realized  in  the  discussions  of  secondary  school 
problems.  The  recommendations  made  are  often  utterly  impossible  of  realiza- 
tion by  the  village  high  school  and  decidedly  unwise  for  the  unlimited  possibility 
high  school.  The  rule  must  in  the  nature  of  the  case  be  that  what  is  best  for 
any  one-fifth  of  high-school  effort  is  not  the  best  for  any  other  fifth. ' ' 


BESULTS  OF  EABLIEB  STUDIES  37 

In  a  study  embracing  46  high  schools  and  36,276  pupils  from 
different  parts  of  the  United  States,  Rounds  and  Kingsbury^  2  j^ave 
suggested  some  correlation  between  the  size  of  school  and  the  quan- 
tity of  promotions  in  English  and  mathematics,  as  in  the  following 
table : 

High  School  Enrolment         ,  Percent  passing  in 

English     Mathematics 

Less  than  400    82.10 .75.55 

From  400  to  800 80.62 74.72 

More  than  80€ 83.23 75.73 

These  writers  find,  however,  great  variation  among  the  school 
of  each  of  these  groups ;  so  great,  in  fact,  that  the  small  differences 
in  central  tendencies  deserve  to  be  given  little  weight. 

Two  intensive  analyses  of  the  high  school  of  the  North  Central 
Association  have  recently  appeared.  The  first  of  these  was  com- 
piled by  Jessup  and  Coffman,i3  the  second  by  Counts.^^As  the  sec- 
ond supersedes  the  first,  and  as  the  methods  pursued  were  very  sim- 
ilar, we  shall  confine  our  review  to  the  latter.  Counts  treats  the  size 
of  1,000  selected  high  schools  as  indicated  in  two  ways ;  by  the  num- 
ber of  students  enroled,  and  by  the  population  of  the  town  in  which 
each  school  is  located.  The  towns  are  grouped  in  seven  groups,  with 
the  following  respective  populations:  under  2,500;  2,501-5,000; 
5,001-7,500 ;  7,501-10,000 ;  10,001-15,000 ;  15,0001-50,000 ;  above  50,- 
000.  As  to  enrolment,  the  schools  are  grouped  under  six  heads,  as 
follows:    1-100,  101-200,  201-300,  301-500,  501-1,000,  above  1,000. 

In  the  first  of  the  accompanying  tables,  both  of  which  are  com- 
piled from  Counts '  results,  is  given  a  summary  of  the  characteristics 
found  to  mark  the  schools  in  towns  and  cities  of  the  different  sizes 
described  in  terms  of  the  median  school  of  each  size.  But  as  Counts 
wisely  observes,  the  median  alone^  is  not  entirely  trustworthy  in  de- 
scribing a  large,  and  particularly  a  varying  group.     Consequently, 


"Rounds,  C.  R.,  and  Kingsbury,  H.  B.  Do  too  many  students  fail?  School 
Beview,  Vol.  21,  585-597. 

"Jessup,  W.  A.,  and  Coffman,'L.  D.  North  Central  High  Schools.  National 
Society  for  the  Study  of  Education.  Thirteenth  Yearbook.  P.  S.  Publishing 
Company,  Bloomington,  111. 

"Judd,  C.  H.,  and  Counts,  G.  S.  Study  of  the  colleges  and  high  schools  of 
the  North  Central  Association.  Bulletin,  United  States  Bureau  of  Education, 
1915,  No.  6. 


88 


TEE  SIXTEENTH  YEARBOOK 


we  shall  accompany  the  table  by  a  brief  verbal  summary  designed  to 
supplement  the  evidence  of  the  medians.  The  second  table  will  be 
similarly  supplemented. 

Table  Showing  Characteristics  of  High  Schools  in  Cities  of  Different  Popula- 
tions (After  Counts) 


Characteristic  of  median  schools  in  cities  of  population  of 


Enrolment 

No.  pupils  per 
teacher 

No.  teachers  per 
school 

Percent  teachers 
inexperienced.  .  . 

Percent  new  teach- 
ers untrained .  . . 

Percent  old  teach- 
ers untrained .  .  . 

Salary,  teachers . . . 

Salary,  prin 

Salary,  supts 

Percent  of  gradu- 
ates who  enter 
college , 

Percent  graduates 
who  go  into 
teaching 

Percent  of  total 
units  of  work  de- 
voted to  English 

Percent  to  Latin.  . 

Percent  to  Mod. 
Language 

Percent  to  Science. 

Percent  to    • 

Mathematics.  . . . 

Percent  to  Hist., 
Civics 

Percent  to  Tech. 
Subjects 

Percent  to 

Commerce 


2,500 
or  less 
T26" 

17 


30.7 
8.9 
4.8 


2,501- 
_5/)00 
~T76" 

19 

9 

30.2 

7.7 


7.4 
$  723    $  765 


1058 
1628 


22.3 

9.1 

14.3 
1L8 

8.6 
11.7 

10.8 

11.6 

22.2 


1140 
1750 


22.3 


14.2 
12.7 

9.0 
11.8 

10.8 

11.5 

23.7 

8.1 


5,001- 
7.500 


210 

20 

11 

22.2 

6.8 

5.2 
!  793 
1292 
1950 

27.4 

3.9 

13.6 
12.6 

9.3 
12.0 

10.6 

1L7 

24.5 

10.0 


7,501- 
10,000 

10,001- 

15,000 

335 

15,001- 

50,000 

^459~ 

273 

20 

21 

21 

13 

15 

22 

28.7 

19.9 

16.9 

7.8 

7.8 

10.1 

7.0 

$  861 

1445 

2000 

4.9 

$  906' 

1587 

2290 

6.1 

$  970 
2005  ! 
2700  1 

29.7 

29.8 

26.0 

3.4 

2.0 

2.3 

12.8 
11.7 

12.1 
11.4 

12.0 
10.5 

10.0 
11.6 

9.7 
11.7 

10.2 
11.6 

9.9 

9.2 

8.8 

11.3 

10.5 

10.4 

26.8 

29.5 

32.1 

10.3 

10.4 

13.9 

and  more 


742 
23 
33 
9.7 

10.6 

8.2 

$1381 

3014 

36.3 

0.6 

ILl 
9.1 

14.8 
11.5 

8.6 

9.3 

29.8 
7.2 


BESULTS  OF  EABLIEB  STUDIES  39 

This  table  affords  data  which  bear  out  the  following  statements : 

1.  The  number  of  pupils  enroled  in  high  school  increases  with 
the  increase  in  city  population,  ''but  it  is  an  interesting  fact  .... 
that,  while  the  large  schools  are  with  hardly  an  exception,  found  in 
the  larger  cities,  the  small  schools  are  by  no  means  confined  to  the 
small  cities.  The  range  of  variation  in  size  of  schools  increases  with 
the  size  of  the  cities"  (p.  39). 

2.  The  number  of  teachers  per  school  does  not  increase  pro- 
portionally to  the  increase  in  enrolment.  Consequently,  the  ratio 
of  pupils  to  teachers  is  higher  in  the  larger  than  in  the  smaller 
towns. 

3.  Schools  in  smaller  towns  and  cities  are  forced  to  accept  an 
undue  proportion  of  inexperienced  teachers. 

4.  The  salaries  paid  to  teachers  in  cities  of  different  sizes  seem 
to  parallel  in  amount  the  experience  of  the  teachers  and  the  number 
of  pupils  whom  they  must  supervise. 

5.  ' '  The  salaries  of  principals  increase  with  the  increase  in  the 
size  of  cities^  much  more  rapidly  than  do  the  salaries  of  teachers ; 
and  the  salaries  of  superintendents  increase  in  about  the  same  fash- 
ion as  the  salaries  of  principals.  These  facts  would  indicate  that  the 
need  for  efficient  administrators  and  supervisors  becomes  increas- 
ingly apparent  as  the  cities  increase  in  size,  while  there  is  no  corre- 
sponding change  in  the  demands  upon  classroom  teachers.'' 

6.  The  larger  the  city,  the  larger  the  proportion  of  its  high- 
school  graduates  who  enter  colleges  and  normal  schools,  or  who  take 
up  business  pursuits,  professional  preparation,  or  the  trades ;  and 
the  smaller  the  proportion  who  enter  commercial  schools,  immediate 
teaching,  farming,  and  other  callings. 

7.  The  larger  the  city,  in  general,  the  less  the  proportionate 
amount  of  school  effort  which  is  given  to  English,  Latin,  mathe- 
matics, history  and  civics ;  and  the  greater  the  proportionate  amount 
devoted  to  modern  languages,  and  technical  and  commercial  sub- 
jects. 

We  now  pass  to  the  second  table. 


40 


THE  SIXTEENTH  TEABJBOOK 


Table  Showing  Characteristics  of  Median  School  Among   Groups  of  Schools 
with  Varying  Enrolments  (After  Counts) 

Characteristics  of  median  of  schools  enroling 


No.  pupils  per 

class 

No.  pupils  per 

teacher 

Periods  taught 

by  supt 

by  prin 

by  teacher 

Study  periods 

supervised 

Value  of  lab. 

equipment 

No.  vols,  in 

library 

Amt.  spent  for 

books  annually .  . . 
Percent  of  total  units 

of  work  devoted 

to  English , 

to  Latin 

to  Mod.  Lang. , ,  . 

to  Science 

to  Mathematics.  . . 

to  Hist,  and  Civ.  . 

to  Tech.  Subjs... 

to  Commerce , 


1-100 


12.5 
11 

1 

4 
4 

0 

$2085 

550 

87 


15.3 
13.0 
12.8 
11.2 
12.2 
12.2 
18.5 
5.6 


101-200 

201-300 
19.5 

301-500 
21 

501-1,000 
22 

17 

18 

21 

22 

22 

1 

0 

0 

0 

4 

3 

2 

0 

5 

5 

5 

5 

4 

5 

6 

8 

$1985 

$2600 

$3875 

$6565 

535 

658 

818 

1288 

86 

97 

112 

145 

14.5 

13.1 

12.0 

10.7 

12.6 

11.9 

11.0 

9.4 

9.3 

8.9 

9.8 

11.7 

11.9 

11.5 

11.4 

11.8 

11.0 

9.8 

9.2 

8.2 

12.0 

11.3 

10.3 

9.6 

21.9 

27.2 

30.1 

33.3 

7.4 

10.4 

11.4 

11.9 

1,000-f- 

24 

26 

0 
0 
5 

13 

$10,755 
2241 
263 


10.0 

7.9 

12.5 

11.9 

7.8 

8.2 

35.6 

8.7 


From  this  table  and  from  the  data  from  which  it  is  drawn,  we 
submit  these  conclusions  and  comments: 

1.  The  size  of  class,  and  the  ratio  of  pupils  pe.r  teacher,  in- 
crease with  the  increase  in  high-school  enrolment.  This  fact,  we 
think,  has  a  most  significant  bearing  upon  existing  studies, ^^ 
which  tend  to  show  that  size  of  class  is  of  comparatively  small  im- 
portance in  determining  school  efficiency.  These  studies,  we  believe, 
by  failing  to  consider  separately  schools  of  different  sizes,  have  ad- 
mitted as  a  complicating  factor  the  superior  facilities  of  the  larger 
schools  which  tend  to  offset  the  effect  of  the  larger  classes  obtaining 
in  these  schools.  Obviously,  studies  of  the  effect  of  size  of  class  upon 
scholarship  can  have  weight  only  when  classes  of  different  size  in 


"Harlan,  C.  L.     Size  of  class  as  a  factor  in  schoolroom  efficiency.   Educa- 
tional Administration  and  Supervision,  Vol.  1,  195-214. 


BESULTS  OF  EABLIEB  STUDIES     '  41 

schools  of  the  same  approximate  size  have  been  considered.    In  the 
study  which  follows,  this  problem  will  be  attacked. 

2.  The  larger  schools  demand  the  whole  time  of  their  prin- 
cipals and  superintendents  for  supervisory  and  administrative  func- 
tions, and  make  correspondingly  larger  demands  upon  their  class- 
room instructors. 

3.  Supervision  of  study  is  practically  ignored  in  the  smaller 
schools. 

4.  The  larger  the  school,  the  better  the  laboratory  and  library 
facilities. 

5.  The  proportion  of  attention  paid  to  the  different  subjects 
of  instruction  varies  among  high  schools  of  different  size  as  among 
cities  of  different  size.  The  smaller  schools  still  give  the  greater 
attention  to  the  traditional  subjects. 

Counts  remarks  in  another  connection  that  ' '  there  seems  to  be 
greater  tendency  for  students  to  leave  school  in  the  larger  cities  than 
in  the  smaller  cities.'' 


CHAPTEE    III 
MATERIALS  AND  METHODS 

The  problems  raised  in  this  investigation  have  already  been 
stated,  but  it  is  desirable  at  this  point  to  recall  them  to  the  reader's 
attention.  To  determine  the  influence  exercised  upon  the  efficiency 
of  a  college  student  by  the  age  at  which  he  enters  college,  and  by  the 
general  character  of  the  high  school  from  which  he  comes ;  that  is 
our  task.  Two  features  constitute  college  efficiency  in  the  meaning 
of  the  present  study;  first,  the  student's  standing  in  his  work,  and 
second,  his  persistence  in  pursuing  his  course  to  the  end. 

Before  undertaking  to  present  the  results  of  our  inquiry  into 
the  influence  exercised  upon  retention  and  scholarship  by  each  of 
the  factors  named,  attention  must  be  called  to  the  materials  upon 
which  these  conclusions  are  founded  and  the  methods  by  which  they 
have  been  reached.  A  discussion  of  these  matters  constitutes  the 
theme  of  the  present  chapter. 

Section  1 

materials 

1.  Fundamental  Materials.  The  original  data  upon  which 
the  investigation  is  based  were  drawn  from  the  registrar's  records 
of  two  different  classes  entering  the  College  of  Science,  Literature, 
and  the  Arts  at  the  University  of  Minnesota  in  1910  and  1911.  These 
classes  include  a  total  of  828  students,  distributed  as  follows : 


Class 

Males 

Females 

Total 

1910 

140 

244 

384 

1911 

189 

255 

444 

Total 

329 

499 

828 

Both  classes  were  traced  throughout  the  four-year  college 
course.  These  registrar's  records  also  furnish  the  necessary  data 
regarding  the  sex  of  the  students,  their  comparative  achievements 
in  scholarship,  and  the  lengths  of  their  college  careers. 

42 


MATEEIALS  AND  METHODS  43 

2.  Accessory  Materials.  Other  sources  of  information  were 
turned  to  for  the  data  regarding  the  size,  in  number  of  pupils  and 
teachers,  of  the  various  high  schools,  and  for  the  high-school  schol- 
arship of  the  students  under  consideration.  The  uses  made  of  these 
data  will  appear  in  our  discussion  of  methods. 

The  reports  of  the  state  high-school  inspector  furnished  the 
necessary  information  regarding  the  high  schools  of  Minnesota,  and 
a  circular  letter  was  sent  to  each  of  the  superintendents  of  the  schools 
involved  outside  the  state,  asking  for  similar  information  regarding 
his  schools  and  teachers.  In  every  case  the  data  were  secured  for 
the  particular  year  in  which  the  students  under  consideration  were 
graduated  from  each  school. 

There  was  also  required  a  statement  of  the  quality  of  the  work 
done  in  the  high  school  by  each  of  the  college  students  recorded,  as 
compared  with  that  done  by  his  high-school  classmates.  Blanks  were 
accordingly  sent  to  each  high  school,  both  in  and  out  of  the  state, 
requesting  a  summary  of  the  marks  earned  during  the  senior  year 
b}^  all  of  the  members  of  every  graduating  class  which  had  sent  one 
or  more  students  to  the  Arts  College  of  the  University  of  Minnesota 
during  the  period  under  consideration.  This  request  was  restricted 
to  the  senior  year  of  the  high-school  course  because  the  scholarship 
shown  during  the  last  year  probably  would  be  more  nearly  typical 
of  the  settled  achievement  of  each  student  than  would  that  shown 
during  the  earlier  pubescent  years.  Furthermore,  different  investi- 
gators have  shown  that  a  considerable  degree  of  continuity  exists 
between  the  scholarship  rank  of  a  pupil  during  one  high-school  year 
and  his  rank  in  preceding  and  succeeding  years.^ 

3.  Evaluation  of  Materials.  Any  attempt  at  original  in- 
vestigation must  carefully  weigh  the  materials  upon  which  its  con- 
clusions are  founded,  as  to  (a)  their  accuracy,  (b)  their  adequacy, 
and  (c)  their  deeper  implications. 

(a)  Accuracy.  There  is  no  reason  to  question  the  accuracy 
of  the  materials  of  the  present  study.  The  registrar's  records,  both 
of  the  University  and  the  high  schools,  are  official  records,  and  are 
as  reliable  as  such  records  anywhere.    The  supplementary  question- 


'See  CJ^pter  I,  Section  2. 


44  TRE  SIXTEENTH  YEAEBOOE 

naires  dealt  with  matters  of  recorded  fact  rather  than  with  matters 
of  opinion,  and  should  be  correspondingly  dependable. 

(b)  Adequacy.  The  different  kinds  of  materials  which  it  was 
necessary  to  collect  could  not  be  made  uniformly  adequate.  The 
number  of  students  for  whom  the  college  records  were  obtained  is 
unusually  large,  so  that  no  apology  need  be  made  for  the  quantity 
of  original  data.  The  data  regarding  size  of  high  school  and  number 
of  teachers  per  school  have  been  made  practically  complete.  But  it 
was  found  impossible  to  make  the  collection  of  high-school  scholar- 
ship records  equally  complete.  We  are  able  to  present  these  stand- 
ings for  only  288  out  of  the  828  students  whose  college  records  were 
compiled.  To  secure  even  this  number,  the  records  of  3,644  high- 
school  graduates  had  to  be  obtained.  With  the  possible  exception, 
then,  of  these  high-school  scholarship  records,  the  data  in  all  cases 
seem  sufficient  in  quantity  to  justify  the  conclusions  based  upon 
them. 

(c)  Implications.  We  now  turn  to  the  problem  of  the  deeper 
significance  of  these  materials.  If  teachers'  marks  are  as  unreliable 
as  many  studies  of  them  would  imply,  and  if  we  are  uncertain  of 
the  causes  which  determine  their  quality,  how  is  it  possible  to  use 
them  as  the  basis  of  a  study  which  seeks  scientific  validity?  In 
reply  we  may  say  that  there  is  a,  quantity  of  evidence  to  show  that 
marks  taken  in  sufficient  numbers  may  be  safely  utilized.  Several 
studies  of  the  distribution  of  school  marks^  indicate  that  the  com- 
posite curve  representing  thousands  of  marks  conforms  within  a 
reasonable  degree  of  variation  to  the  normal  or  binomial  curve.  For 
this  reason  it  has  been  held  that  such  masses  of  marks  portray  with 
considerable  accuracy  some  biological  function.  Again,  a  continuity 
has  been  shown  to  exist  between  the  rank  held  by  a  student  in  the 
high  school  and  the  position  which  he  later  occupies  in  the  college. 
A  similar  continuity  between  rank  in  the  elementary  school  and  the 
high  school,  and  in  the  grammar  school,  the  high  school,  and  the  col- 
lege, has  been  established.^  As  the  positions  of  these  students  were 
in  every  case  determined  upon  the  basis  of  school  marks,  the  impli- 
cation is  that  a  continuity  exists  among  the  marks  themselves  which 


-See  Chapter  T,  Section  1. 
*See  Chapter  I,  Section  2. 


MATERIALS  AND  METHODS 


45 


can  hardly  be  the  product  of  accident.  A  third  thread  of  evidence  is 
found  in  the  fact  that  a  student  who  ranks  high  in  one  line  of  school 
activity  is  very  likely  to  rank  high  in  other  lines. ^  Here,  again,  all 
of  the  rankings  have  been  based  upon  school  and  college  marks,  and 
the  same  implications  must  follow  regarding  the  reliability  of  these 
marks  when  taken  in  sufficient  numbers.  The  statistical  usefulness 
of  a  body  of  material  does  not  require  that  we  know  at  the  begin- 
ning the  laws  operating  within  the  material,  but  simply  that  we 
have  reason  to  suppose  that  it  does  follow  some  law.  The  gist  of 
this  accumulated  evidence  is  that,  whatever  may  be  the  causes  deter- 
mining the  quality  of  school  marks,  these  marks  are  sufficiently 
reliable  for  statistical  purposes  if  there  be  enough  of  them. 

The  present  study  embraces  more  than  20,000  college  scholarship 
marks,  by  actual  count,  and  almost  an  equal  number,  estimated,  of 
high-school  marks.  Table  1  and  Graph  I  show  the  form  of  the  dis- 
tribution of  the  college  scholarship  marks.  The  curves  for  both 
sexes  are  skewed  strongly  toward  the  high  end  of  the  marking  scale, 
but  the  females,  upon  the  whole,  earned  considerably  the  better 
marks. 


TABLE  I 

Showing  the  Distribution  of  20,090  College  Scholarship  Maries  for  Both  Sexes 
and  for  Each  of  the  Fo^r  College  Years 


Excellent  |    Good 

Passed 

Condition 

Failed 

Freshmen 

Males :    Number 

333 
12.4 

852 
20.9 

890 
33.3 

1578 
38.5 

840 
31.4 

1216 
29.9 

297 
11.1 

240 
5.9 

313 

Percent 

11.7 

Females :    Number 

Percent 

180 
4.8 

Sophomores 

Males :    Number 

Percent 

249 
13.1 

856 
21.8 

661 
34.8 

1680 
42.9 

632 
33.3 

1058 
27.2 

182 
9.6 

232 
5.9 

171 
9.0 

Females :    Number 

Percent 

82 
22 

*See  Chapter  I,  Section  2. 


46 


THE  SIXTEENTH  YEABBOOK 


Juniors 


Males :    Number 

287 
23.2 

674 
19.6 

526 
42.6 

1730 
50.3 

310 
25.1 

858 
25.0 

76 
6.2 

128 
3.7 

35 

Percent 

2.9 

Females:    Number 

Percent 

46 
1.4 

Seniors 


Males  •    Number 

132 
30.0 

584 
23.6 

192 
43.6 

1470 
59.5 

90 
20.5 

380 
15.4 

14 
3.2 

28 
1.1 

12 

Percent 

2.7 

Females :    Number 

Percent 

10 
0.4 

All 

Years 

Males:    Number 

Percent 

1001 
16.0 

2269 
3.63 

1872 
29.9 

569 
9.1 

531 
8.5 

Females :    Number 

Percent 

2966 
21.3 

6458 
46.5 

3512 
25.3 

628 
4.4 

318 
2.5 

GEAPH  I. 

Distribution  of  20,090  College  Scholarship  Marks,  Without  Eeference  to 
THE  College  Year  During  Which  the  Marks  were  Earned. 
so 


1 


t 


I 


40 


3o 


ao 


' 

1 

1 

1 

> 

1 

1 
1 

1— — 

1 

t 

t 

\ 



- 

l—~" 

C  5P 

ScLolorshuip  /nar-tfg 


~f%rno»\p&   —  .^  «.  _ 


MATEBIALS  AND  METHODS  47 

Section  2 
methods  of  studying  college  materials 

1.  General  Considerations.  During  the  early  stages  of  the 
investigation,  each  of  the  two  entrance  classes,  entering  in  1910  and 
1911,  respectively,  was  studied  separately.  Each  entrance  class 
is  logically  a  sort  of  competitive  group,  and  the  members  of  classes 
entering  college  in  different  years  may  not  earn  their  marks  under 
conditions  quite  identical.  However,  as  this  separate  treatment  of 
the  two  classes  did  not  appear  to  be  yielding  results  commensurate 
with  the  time  it  required,  it  was  discontinued  during  the  later 
stages. 

Throughout  the  study  the  two  sexes  have  been  treated  sepa- 
rately. It  may  be  permissible  to  combine  the  sexes  in  studies  having 
to  do  with  the  pre-adolescent  period,  although  the  wisdom  of  such 
a  course  is  doubtful  even  then,  but  in  investigations  having  to  do 
with  high-school  and  college  students,  such  a  method  is  almost  sure 
to  lead  to  serious  error.  In  some  of  the  results  here  rendered  the 
males  and  females  show  considerable  uniformity,  but  in  other  in- 
stances there  appear  very  decided  differences. 

As  has  been  said,  two  measures  of  comparative  efficiency  are 
utilized  in  this  investigation.  The  first  is  the  quality  of  scholarship 
shown  by  the  marks  each  student  received ;  the  second  is  the  length 
of  time  which  each  student  remained  at  college  work.  The  methods 
pursued,  in  the  application  of  each  of  these  measures  will  now  be 
described. 

2.  MetJiods  pursued  in  ranking  students  as  to  scJiolarsliip. 
Most  of  the  scholarship  comparisons  have  been  made  by  means  of  the 
ranking  method.  This  method  consisted  of  five  steps:  (a)  finding 
the  total  number  of  marks  of  each  denomination  earned  by  each 
student  in  each  year  of  his  college  course;  (&)  ascribing  to  each 
mark  the  numerical  value  stated  in  a  succeeding  paragraph;  (c) 
finding  the  sum  of  these  numerical  equivalents  in  each  pupil's  an- 
nual record;  (d)  ranking  the  students  of  each  entrance  age,  etc., 
in  order  of  merit  from  highest  to  lowest  according  to  these  sums; 
and  (e)  finding  the  median  pupil,  and  the  first  and  third  quartile 
pupils,  in  the  groups  representing  the  different  entrance  ages,  sizes 


48  TEE  SIXTEENTH  YEARBOOK 

of  high  school,  etc.  The  special  features  of  each  step  are  next  de- 
scribed. 

(a)  The  marks  totaled  in  the  first  step  were  the  five  marks 
in  use  in  the  College  of  Science,  Literature,  and  the  Arts  in  the  Uni- 
versity of  Minnesota  during  the  period  covered  by  the  investigation. 
These  marks  were  in  the  form  of  letters;  B,  G.  P,  C,  and  F.  Of 
these,  E,  G,  and  P  represented  ''excellent",  ''good",  and  "passed", 
respectively;  C  represented  a  "condition",  which  might  be  removed 
by  special  examination  or  by  partial  repetition  of  work ;  and  F  rep- 
resented a  complete  failure.  Only  one  other  mark,  that  of  I,  or  "in- 
complete", appeared  upon  the  records.  In  cases  where  this  mark 
had  not  been  removed  by  the  later  passing  of  the  course  it  was 
changed  to  failure;  where  it  had  been  removed  the  student  was 
credited  with  the  mark  received  on  its  removal.  The  term  "mark" 
as  here  used  means  one  semester's  grade  in  one  subject  for  the  col- 
lege, and  one  term's  grade  in  one  subject,  for  the  high  school. 

(&)  The  second  step  in  the  process  of  ranking  required  the 
substitution  of  a  numerical  value  for  each  of  the  college  marks.  The 
values  selected  were  the  following : 

F  =  — 1 
C  =  0 
P  =  1 
G  =  2 
E  r=       3 

The  mark  C  was  given  the  value  of  zero  because  C  represents 
no  recognized  progress  toward  graduation ;  P  was  given  the  value 
plus  1  because  it  represents  one  unit  of  such  progress ;  and  F  was 
given  the  value  minus  1  because  it  must  be  removed  later  by  the 
student's  retaking  and  parsing  the  subject  in  which  it  was  received, 
or  by  presenting  an  acceptable  substitute.  G  was  valued  at  plus  2 
and  E  at  plus  3  in  order  that  the  distances  between  the  different 
units  might  remain  uniform.^ 

(c)  The  procedure  in  Step  3  was  very  simple,  consisting  only 
in  summing  up  the  numerical  equivalents  for  the  marks  earned  by 
each  student  during  each  college  year. 


^The  writer  acknowledges  Ms  indebtedness  to  an  unpublished  study  by 
Professor  David  P.  Swenson,  of  the  University  of  Minnesota,  for  the  numerical 
equivalents  here  utilized. 


MATEBIALS  AND  METHODS  49 

Various  eliminations  of  marks,  however,  were  found  to  be  nec- 
essary. Work  performed  during  summer  school  was  not  counted. 
All  * '  no-credit ' '  courses  were  excluded.  Only  the  first  mark  given 
a  student  in  a  subject  was  considered,  in  all  those  cases  where  the 
subject  had  been  repeated  in  order  to  raise  the  mark  first  received. 
In  all  such  cases,  except  those  originally  marked  *' incomplete ' ',  no 
notice  was  taken  of  later  marks,  which  were  interpreted  as  concerned 
with  a  second  set  of  facts  not  to  be  considered  here. 

(d)  Step  4  is  more  intricate  and  much  more  difficult  to 
describe.  Let  us  therefore  make  it  concrete.  First  we  separated  the 
data  for  the  entrance  classes,  and  started  with  the  class  entering  in 
1910.  This  class  was  then  divided  into  two  groups  upon  the  basis 
of  sex.  Next,  each  of  these  sex  groups  was  divided,  upon  the  basis 
of  age  at  entrance,  or  of  character  of  high  school.  In  the  former 
case  we  would  have,  for  instance,  the  males  and  females  each  brought 
into  groups  representing  the  17-year-old  entrants,  the  18-year-old 
entrants,  etc.  The  members  of  each  of  these  age-groups  were  then 
ranked  in  order  from  highest  to  lowest,  according  to  the  sums  of  the 
numerical  equivalents  assigned  to  the  marks  of  each  student.  Four 
separate  rankings  were  thus  made  for  each  group,  one  for  each  col- 
lege year. 

(e)  In  Step  5,  the  median  pupil  was  found  for  each  group, 
for  each  college  year,  and  the  numerical  value  of  the  scholarship 
marks  of  this  pupil  was  taken  as  the  index  of  the  scholarship  of 
that  group  for  the  given  college  year.  Comparison  of  the  scholar- 
ship efficiency  of  the  17-year-old  entrants  with  the  18-year-old  en- 
trants,etc.,  was  made  by  means  of  these  median  equivalents.  The 
range  of  variation  in  each  group  was  also  found  in  terms  of  the 
' '  middle  50  percent. ' ' 

This  process  was  repeated  for  the  class  entering  in  1911.  As  a 
result  we  finally  reach  a  statement  of  the  median  scholarship  of  the 
students  entering  at  17,  18,  19,  20,  21,  etc.,  years  of  age  for  each 
sex  and  each  college  year,  and  for  each  of  the  two  entrance  classes. 
We  also  have  a  statement  of  the  range  of  the  middle  50  percent  for 
each  of  these  several  groups. 

The  above  procedure  was  duplicated  in  studying  the  scholar- 
ship achievements  of  students  entering  from  the  different  types  of 


50  TEE  SIXTEENTH  YEARBOOK 

high  schools,  except  that  character  of  high  school,  rather  than  age 
at  entrance  was  used  to  determine  membership  in  each  comparative 
group. 

3.  Metliods  pursued  in  comparing  tJie  lengtJis  of  tJie  students' 
college  careers.  In  general,  the  different  student-groups  described 
above  were  compared  as  to  the  percentage  of  members  eliminated  at 
different  stages  of  the  college  course,  usually  at  the  end  of  each  col- 
lege year.  The  number  of  semesters  during  which  the  median  mem- 
ber of  each  group  remained  in  college  was  also  used.  All  students 
were  regarded  as  ''eliminated"  who  were  dropped  from  the  rolls 
of  the  College  of  Science,  Literature,  and  the  Arts  before  the  end 
of  the  course,  and  who  did  not  reappear  upon  them.  Such  students 
as  left  the  college  to  enrol  in  some  other  department  of  the  Univer- 
sity of  Minnesota,  as  Law,  Medicine,  Agriculture,  and  Engineering, 
were  included  among  the  eliminations,  but  a  statement  of  their  num- 
ber has  been  appended.  It  was  found  impossible  to  ascertain  the 
number  of  those  who  left  the  University  of  Minnesota  to  enrol  in 
some  other  institution. 

4.  Evaluation  of  MetJiods.  Several  features  of  the  methods 
which  have  just  been  described  may  invite  criticism. 

First,  objection  is  anticipated  to  the  fact  that  equal  weight  has 
been  attached  to  marks  of  the  same  denomination,  irrespective  of  the 
teachers  who  gave  them.  The  writer  is  perfectly  aware  that  the 
marks  of  the  different  teachers  do  not  mean  the  same  thing.  The 
G  of  one  teacher  is  not  always  equal  to  the  G  of  another  teacher. 
Some  teachers  are  notoriously  high  markers,  and  others  are  notor- 
iously low  markers.  But  in  spite  of  these  admitted  differences,  the 
marks  of  different  teachers  have  been  treated  as  equivalents  for  sev- 
eral reasons. 

In  the  first  place,  the  data  were  not  accessible  which  would  be 
necessary  if  one  were  to  take  strict  account  of  teachers'  individual 
differences.  The  proper  procedure,  from  this  point  of  view,  would 
be  to  rank  the  members  of  each  recitation  group,  under  each  indi- 
vidual instructor's  marks.  Later  group  rankings  would  then  be 
found  by  combining  the  rankings  given  by  the  individual  instruc- 
tors. But  such  a  procedure  was  impractical,  in  the  present  instance, 
because  the  registrar 's  records  of  the  university  did  not  take  account 


MATEBIAL8  AND  METHODS  51 

of  individual  teachers.  The  nearest  possible  approach  would  have 
been  to  find  the  rankings  in  separate  subjects,  but  this  would  by 
no  means  have  avoided  the  difficulty,  for  usually  more  than  one  in- 
structor teaches  the  same  subject. 

In  the  second  place,  inspection  of  the  data  fails  to  reveal  any 
noticeable  correlation  between  age  at  entrance  or  character  of  high 
school  and  the  departments  in  which  the  students  elected  to  do  most 
of  their  college  work.  Nor  is  there  any  evident  reason  for  expecting 
such  a  correlation.  In  fact,  a  thorough  study  of  the  freshmen  of 
one  entrance  class,  dealing  with  the  influence  of  age  at  entrance 
upon  scholarship  in  the  separate  fields  of  English,  mathematics,  sci- 
ence, and  history,  brings  out  tendencies  in  each  field  exactly  like 
those  shown  when  the  marks  were  treated  erv  masse. 

Finally,  the  method  here  employed  does  not  necessarily  assume 
that  different  teachers  mean  the  same  thing  by  the  same  mark.  What 
it  does  assume  is  that  in  the  long  run  the  low  markers  and  the  high 
markers  strike  a  fairly  even  balance.  The  error  introduced  is  of 
the  compensating  and  not  of  the  cumulating  sort.  But  even  if  it 
were  assumed  that  identical  scholarship  marks  possessed  identical 
values,  the  example  of  every  college  and  university  which  requires  a 
student  receiving  a  failure,  no  matter  from  what  instructor,  to  re- 
peat his  work,  and  which  passes  every  student  marked  ''passed" 
and  above  by  any  and  every  teacher,  might  be  pointed  to  as  in  a 
measure  justifying  that  assumption. 

The  present  study  has  departed  from  the  usual  plan  of  averag- 
ing the  marks  earned  by  a  student  during  a  given  year  in  order  to 
secure  a  measure  of  his  scholarship.  This  study  substitutes  the  sum 
of  these  marks  for  their  averages.  The  reason  for  adopting  this 
procedure  is  as  follows : 

The  writer  wishes  to  compare  the  scholarship  shown  by  the  dif- 
ferent students  in  all  of  their  work  for  each  college  year.  He  is  con- 
cerned with  their  entire  college  accomplishment  on  record  for  each 
year.  He  does  not  wish  to  enter  into  the  problem  of  comparative 
efficiency  in  different  lines  of  subject  matter.  If  he  were  to  average 
the  marks  earned  by  each  student  during  the  whole  college  year,  he 
would  give  weight  to  quality  only,  and  would  take  no  account  of 
differences  in  the  number  of  courses  completed.  He  would  thus  put 
the  student  who  carried  two  courses  upon  the  same  plane  with  the 


52  THE  SIXTEENTH  YEARBOOK 

one  who  carried  five,  provided  that  the  quality  of  work  done  in  the 
two  cases  was  the  same. 

A  striking  example  of  this  danger  came  to  light  in  the  course 
of  the  compilation.  Two  students  were  found,  whom  we  may  desig- 
nate as  A  and  B,  each  of  whom  had  received  a  mark  of  G  in  rhetoric, 
German  and  chemistry.  A  carried  only  these  three  subjects ;  B  had 
also  entered  a  course  in  mathematics  from  which  he  emerged  with' 
a  mark  of  P.  If  these  marks  had  been  averaged,  B  would  have  ap- 
peared as  inferior  to  A,  although  he  had  received  identical  marks 
in  all  of  the  subjects  taken  by  A,  and  had  carried  and  passed  one 
subject  more.  Clearly,  the  only  way  to  treat  such  a  situation  is  to 
consider  both  quantity  and  quality ;  that  is,  to  total  the  marks. 

However,  it  may  be  said  that  consideration  of  the  averages  of 
the  marks  in  place  of  their  totals  would  have  made  no  marked  change 
in  the  results.  Inspection  of  Table  2,  which  is  based  upon  95  cases 
selected  so  as  to  represent  all  degrees  of  scholastic  efficiency,  demon- 
strates that  the  students  who  ranked  high  in  the  totals  also  ranked 
high  in  the  averages;  and  conversely.  Furthermore,  the  place  of 
each  individual  in  each  of  the  two  series  is  almost  identical.  The 
rank-difference  coefficients  are  as  follows:  males  0.98  ±  .01;  fe- 
males, 0.96  ±  .01. 

A  third  possible  source  of  error  consists  in  the  fact  that  equal 
weight  has  been  given  to  every  mark  of  the  same  denomination,  re- 
gardless of  differences  in  the  number  of  hours  per  week  which  the 
various  courses  demanded.  Thus  Rhetoric  1  is  a  three-credit  course, 
meeting  three  hours  per  week,  while  Mathematics  1  is  a  five-credit 
course,  meeting  five  hours  per  week.  Yet  the  study  treats  a  G 
earned  in  Rhetoric  1  as  equivalent  to  a  G  earned  in  Mathematics  1. 

This  is  clearly  not  the  perfect  procedure,  and  can  be  justified 
only  by  its  economy,  and  by  the  fact  that  the  error  involved  is  prac- 
tically insignificant.  Its  insignificance  is  demonstrated  in  Table  3. 
This  table  compares  the  respective  positions  of  95  students  selected 
so  as  to  represent  all  degrees  of  scholastic  efficiency,  in  two  serial 
orders.  The  first  series  for  each  sex  states  the  sum  of  the  numerical 
equivalents  of  the  marks  earned  by  each  student,  before  these  marks 
had  been  weighted  to  take  account  of  hour-differences.  The  second 
series  shows  the  corresponding  value  for  each  pupil,  when  each  mark 
had  been  weighed  according  to  the  number  of  hours  required  for  the 


MATERIALS  AND  METHODS 


53 


TABLE  2 

Comparison  of  Total-Marie  Equivalents  with  Average-Marie  Equivalents  as 
Measures  of  Scholarship  During  the  Freshman  College  Year 

(Only  enough  cases  are  given  to  serve  as  samples  in  different  ranges.) 


Individual 
1 

Males 
Totals 

—8.0 

—8.0 

—6.0 

—6.0 

—2.0 

—1.0 

0    

0    

2.0 

2.0 

4.0 

10.0 

10.0 

11.0 

20.0 

20.0 

22.0 

23.0 

26.0 

30.0 

Averages 
. — 1.0     

Individus 
1  .. 

Females 
al          Totals 

— 8.O.... 

—8.0... 

— 4.O.... 

0    ... 

2.0... . 

5.0... 

6.0... 

7.0... 

7.0... 

8.0... 

9.0... 

13.0... 

13.0... 

14.0... 

24.0... 

25.0... 

26.0... 

27.0... 

28.0... 

30.0... 

Averages 
. .  .—1.0 

2 

, — 8  0     . 

2  .. 

. .  .—1.0 

3 

.—1.0     

3  .. 

...—1.0 

4 

.—0.75  

4  .  . 

...     0 

5 

.—0.40   

5  .  . 

. . .     0.25 

6 

.__0.20   

6  .  . 

. . .     0.71 

7   

.     0       

7  .. 

. . .     0.67 

8 

.     0        

8  .. 

. . .     0.875 

9 

.     0.33  

9  .  . 

.  . .     1.16 

10 

11 

.     0.25   

.     0.50   

10  . . 

11  .. 

.  . .  0.89 
.  . .     1.125 

22 

1 00       

22  .. 

. . .     1.30 

23 

24 

41 

42 

43   

44 

45 

46 

.     0.91   

.     1.10  

.     2.00 

.     2.00 

.     2.20   

.     2.30   

.     2.89   

.     3.00   

23  .. 

24  .. 

44  .. 

45  .. 

46  .. 

47  .. 

48  .. 

49  .. 

. . .  1.62 
. . .     1.75 

. . .  2.18 
. . .  2.50 
. . .  2.70 
. . .  2.70 
. . .  2.80 
.  . .     2.50 

course  in  which  it  was  earned.  Thus,  a  P  in  a  three-hour  subject 
was  counted  as  3,  and  a  P  in  a  five-hour  subject  as  5.  Inspection 
ai  the  table  reveals  a  surprising  similarity  in  the  positions  of  almost 
every  student  in  the  two  series.  Expressed  in  terms  of  the  rank- 
difference  formula,  we  have  for  the  males  a  coefficient  of  0.98  ±  .01 ; 
and  for  the  females  a  coefficient  of  0.97  ±  .01.  The  error  arising 
from  failure  to  weight  the  grades  for  number  of  hours  per  week 
may,  therefore,  be  regarded  as  practically  negligible. 


THE  SIXTEENTH  YEABBOOK 


TABLE  3 

A  comparison  of  the  Total  Marie  Equivalents  when  Maries  were  Unweighted, 
with  Equivalents  when  Each  Mark  was  Weighted  According  to  the  Number  of 
Hour-Credits  Earned  in  Each  Subject. 

(Only  enough  cases  are  given  to  serve  as  samples  in  the  different  ranges.) 


Males 

Females 

Indi- 

Not 

Indi- 

Not 

vidual 

Weighted 

Weighted 

vidual 

Weighted 

Weighted 

1 

.    .  —8 

.—32 
.—18 

1  .... 

2  .... 

...  —8...... 

...  —8 

. ..  —32 

2   .... 

.  ..  —8 

. ..  —28 

3 

.  ..  —6 

. ..  —6 

.—22 
.—22 

3  .... 

4   

.  , .  — 4 

. . .  —16 

4 

...       0 

. ..     —2 

5   .... 

...  —2 

.   —8 

5   .... 

1 

3 

6   .... 

. ..  — 1 

.  —1 

6   .... 

5 

...       12 

7 

...       0 

0 

.        1 
0 

7    .  . .  . 

6 

13 

8 

8   .... 

...       7 

...       25 

9 

...       0 

...       2 

.     10 
.       6 

9   

8 

23 

10   .... 

10   .... 

...       9 

. . .       37 

11   .... 

2.. 

.     14 

11 

...       9 

...       31 

23   .... 

. ..     10 

.     27 

23   .... 

...     13 

49 

24   .... 

...     10 

.     37 

24   .... 

...     14 

. ..       54 

25   .... 

. ..    11 

.     39 

25   .... 

...     14 

...       50 

42   .... 

. ..     20 

.     57 

44   .... 

...     24 

...       74 

43   

...     22 

. ..     23 

.     66 
.     64 

45   

.  .  .     25 

75 

44   .... 

46   .... 

...     26 

...       72 

45   .... 

. ..     26 

.     82 

47   .... 

...     27 

81 

46   .... 

. ..     30 

.   102 

48   .... 

...     28 

...       96 

47   .... 

49    .... 

...     30 

...       86 

CHAPTER  IV 

ENTRAJ^CE  AGE  AS  RELATED  TO  COLLEGE  EFFICIENCY 

This  chapter  deals  with  the  comparative  scholarship  and  per- 
sistence of  the  groups  who  entered  at  various  ages,  i.  e.,  of  the  17- 
year-old,  the  18-year-old,  the  19-year-old,  etc.,  entrants.  The  17- 
year-old  entrants  include  students  whose  ages  at  the  time  of  entering 
college  ranged  from  16  years,  6  months,  to  17  years,  6  months.  The 
18-,  19-,  and  20-year-old  entrants,  etc.,  each  cover  similar  ranges. 

The  percentages  of  the  students  who  entered  at  different  ages 
are  sho^vn  in  Table  4. 

TABLE  4 

Percentage  of  College  Entrants  at  Each  Age 


Age  at 
Entrance 

Males 

Females 

Class 

Class 

Both 

Class 

Class 

Both 

1910-11 

1911-12 

Classes 

1910-11 

1911-12 

Classes 

16 

2.2 

2.8 

2.5 

1.6 

0.8 

1.2 

17 

8.8 

9.8 

9.2 

9.1 

8.7 

8.8 

18 

20.6 

26.2 

24.5 

38.2 

36.5 

37.2 

19 

32.3 

29.3 

30.2 

28.9 

30.2 

29.2 

20 

22.1 

15.9 

18.4 

10.9 

15.8 

13.5 

21 

5.1 

9.3 

7.6 

6.6 

3.9 

5.3 

22 

4.4 

2.7 

3.2 

1.6 

1.8 

1.8 

23 

2.4 

1.6 

1.9 

0.4 

0.4 

0.4 

24 

0.7 

0.6 

0.7 

0.9 

0.5 

25 

0.7 

0.6 

0.7 

0.4 

0.2 

26 

1.2 

0.7 

0.4 

0.8 

0.7 

27 

28 

0.4 

0.2 

29 

0.7 

0.4 

0.8 

0.4 

30 

0.4 

0.4 

35 

0.4 

0.4 

0.2 

This  table  shows  an  extreme  range  in  entrance-age  of  from  16 
to  29  for  the  males,  and  from  16  to  35  for  the  females.  Eighteen 
appears  to  be  the  modal  entrance  age  for  the  females  and  19  for  the 
males.  The  median  in  both  sexes  is  19 ;  the  average  for  the  males 
is  19.2,  with  a  mean  variation  of  1.22 ;  for  the  females,  18.9,  M.  V., 
1.12.    The  females  were  on  the  whole  three  tenths  of  a  year  younger 

55 


56  THE  SIXTEENTH  YEAEBOOK 

than  the  males  when  both  began  their  college  work.  Despite  the 
wider  range  in  the  females,  comparison  of  the  average  variations 
shows  that  males  were  marked  by  the  greater  variability  in  entrance 
ages. 

Section  1 

comparison  of  the  scholarship  marks  of  the  groups  entering 
at  different  ages 

The  methods  pursued  in  making  these  comparisons  have  been 
described  at  length  in  Chapter  III.  It  is  necessary  at  this  point 
only  to  interpret  the  tables  and  graphs  containing  the  results. 

The  reader  is  invited  to  turn  first  to  the  accompanying  tables, 
and  to  observe  the  following  points.  Tables  5  to  7  show  the  num- 
ber of  males  belonging  to  each  of  the  different  entrance-age  groups, 
during  each  college  year,  and  the  comparative  scholarship  of  each 
age-group ;  these  data  are  presented  separately  for  the  two  entrance 
classes  (Tables  5  and  6),  and  for  both  classes  combined  (Table  7). 
Tables  8  to  10  present  similar  data  organized  in  like  fashion  for  the 
female  entrants.  Comparative  scholarship  is  stated  in  terms  of 
(1)  the  range  between  the  number  representing  the  total  numerical 
equivalent  of  the  marks  of  the  lowest  pupil  in  each  group,  and  the 
number  representing  the  marks  of  the  pupil  standing  highest  in 
each  group;  (2)  the  range  between  the  number  representing  the 
pupil  occupying  the  first  quartile  position  and  the  number  for  the 
pupil  occupying  the  third  quartile  position  in  each  group  ;  (3)  and 
the  number  representing  the  total  equivalents  of  the  marks  earned 
by  the  median  pupil  in  each  group.  The  median  as  thus  described 
will  be  taken  as  the  standard  measure  of  central  tendency,  and  the 
range  of  the  middle  50  percent  as  the  standard  measure  of  varia- 
tion, in  that  part  of  our  study  which  is  concerned  with  comparisons 
of  efficiency  as  shown  by  scholarship  marks. 

It  has  not  seemed  desirable  to  attempt  to  present  all  of  these 
features  in  the  graphs.  The  median,  being  the  measure  of  central 
tendency,  is,  of  course,  the  fundamental  unit  of  comparison,  and 
must  be  portrayed.  The  range  of  the  middle  50  percent  or  the  in- 
terquartile range,  is  of  considerable  assistance  in  interpreting  the 
median,  and  often  in  qualifying  or  elaborating  inferences  based 


ENTRANCE  AGE  AS  BELATED  TO  COLLEGE  EFFICIENCY       57 

upon  it.  But  no  significant  purpose  would  be  served  by  an  attempt 
to  portray  the  extreme  range  in  scholarship  shown  by  each  group, 
since  the  numerical  values  representing  these  extremes  are  often,  if 
not  always,  accidental. 

The  reader's  attention  is  now  directed  to  Graph  II. ^  Let  us 
offer  a  concrete  interpretation.  This  graph  describes  the  scholar- 
ship achievements  of  the  freshmen  who  entered  at  different  ages; 
the  males  are  represented  on  the  left  side  of  the  graph,  and  the  fe- 
males on  the  right.  Note,  for  illustration,  the  male  curves.  The 
heavy  black  curve  represents  the  males  of  both  entrance  classes 
combined,  and  shows  that  the  numerical  value  of  the  marks  earned 
by  the  median  pupil  of  the  group  who  entered  at  sixteen  was  14, 
of  the  group  who  entered  at  seventeen  was  16,  etc.  After  eighteen, 
the  curve  is  seen  to  turn  rapidly  toward  the  base  until  twenty-two, 
after  which  it  becomes  generally  normal  again,  indicating  that  the 
median  students  of  the  groups  entering  at  ages  from  19  to  22,  stood 
lower  in  scholarship  than  those  of  the  groups  entering  before  and 
after  these  ages.  The  25-year-old  entrance  group  is  a  conspicuous 
exception.  The  horizontal  broken  lines  represent  the  range  of  the 
middle  50  per  cent,  all  male  entrants  considered.  This  is  seen  to 
follow  the  general  tendency  displayed  by  the  median.  The  dotted 
and  broken  lines  represent,  respectively,  the  medians  of  the  different 
age-groups  in  the  entrance  classes  of  1910  and  1911. 

The  curves  on  the  right-hand  side  of  the  graph,  representing  the 
female  freshmen,  may  be  interpreted  in  like  manner.  The  most 
noticeable  feature  here  is  that  the  drop  indicating  a  decline  in  schol- 
arship from  19  to  22,  while  present,  is  much  less  pronounced  than  in 
the  case  of  the  males. 

Graphs  III,  IV,  and  V  are  all  to  be  interpreted  like  Graph  II. 
These  three  graphs  represent  the  sophomore,  junior,  and  senior  at- 
tainments of  the  entrants  of  different  ages.  Graph  VI  brings  to- 
gether, for  purposes  of  closer  comparison,  the  heavy  black  curves,  or 


^The  reader  will  note  that  in  this  and  all  succeeding  graphs  the  curve  rep- 
resenting scholarship  merit  runs  vertically,  rather  than  horizontally.  In  other 
words,  scholarship  values  are  represented  on  the  abscissae,  rather  than  on  the 
ordinates,  the  latter  being  used  to  represent  entrance  ages,  etc.  The  writer  has 
two  reasons  for  adopting  this  form :  first,  the  graphs  are  thus  made  to 
correspond  structurally  to  the  tables;  and  second,  this  is  the  only  graphic 
method  which  can  be  used  consistently  in  all  parts  of  the  study. 


58 


THE  SIXTEENTH  YEABBOOK 


'Hotal"  curves,  of  each  of  the  other  graphs.  Inspection  of  this  figure 
brings  out  the  changes  going  on  from  year  to  year. 

We  can  best  summarize  the  conclusions  from  these  tables  and 
graphs  under  two  heads ;  first,  the  differences  in  scholastic  achieve- 
ment marking  the  different  age-groups  during  the  freshman  year ; 
and  second,  the  changes  that  appear  in  the  course  of  the  succeeding 
college  years.  Emphasis  is  put  upon  the  differences  appearing  dur- 
ing the  freshman  year,  because  this  was  the  only  year  in  which  all 
college  entrants  were  in  actual  competition.  Qualitative  elimination 
becomes  a  disturbing  factor  later. 

FRESHMAN  DIFFERENCES 

1.  Males  entering  at  ages  from  19  to  21  or  22  stood  lower  in 
scholarship  than  those  entering  younger. 

2.  The  same  general  tendency  appears  among  the  females,  but 
not  to  the  same  degree,  nor  so  consistently. 

3.  After  22  the  scholarship  curves  are  extremely  variable, 
owing  to  the  small  number  of  cases,  but  they  suggest  somewhat  bet- 
ter attainments. 

TABLE    5 

Comparative  Scholarship,  During  Successive  College  Tears,   of  Male   Students  Entering 
College  in  1910  at  Different  Ages. 

Scholarship  stated  in  terms  of  numerical  equivalents  of  marks  earned  by  the  median 
student,  the  first  and  third  quartile  student,  and  the  best  and  poorest  students  of  each 
entrance  age  group. 


2  S       u      M '  Median 

a  g  «  J      fl '  Schol 
•Si-^jS  o'S!arship 


oil 


Range  of 

Middle  50 

percent 


1st 
Quar- 
tile 


3d 
Quar- 
tile 


16 
17 
18 

19 

20 
21 

22 
23 
24 

25 
26 
27 

28 
29 


3 

12 
30 

43 
29 

7 


18 
13 
11.5 

12 
4 


4 
16 
26 


17 


7.5 
2.75 


19.75 
17.5 

16 
13 
19 

13.5 


Range  of 
Scholar- 
ship 
Values 


12  to  26 

lto26 

-6  to  30 

-8  to  23 
-8  to  23 

6  to  20 

-6  to  18 

7  to  23 


Sophomores 


^      rin 


8 
21 

27 

13 

5 

2 

i 


Median 
Schol- 
arship 


22 
14 
13 

10 


Range  of 

Middle  50 

percent 


1st 
Quar- 
tile 


11.50 
5.5 

8 

,   2 

5 


3d 
Quar- 
tile 


Range  of 

Scholarship 

Values 


17.75 
20 

19 

22.5 

15 


4  to  24 
-8  to  25 
-8  to  30 

lto26 
2  to  29 
4  to  19 

7  to  15 


ENTRANCE  AGE  AS  BELATED  TO  COLLEGE  EFFICIENCY 


59 


Juniors 


Seniors 


16 
17 

18 

19 

20 
21 

22 
23 
24 

25 
26 
27 

28 
29 


3 

7 

13 

21 
19 

20 

18  '  ' 
10 

26 

13 

8 
2 

17 

25 
17 

4.5 
10.75 

24.5 
33.25 

1 

18 



26 

.... 

.... 

'■[ 

16  '  ' 

.... 

.... 

3  to  29 

10  to  29 

5  to  31 

-4  to  30 

0to35 

14  to  20 


2 

5 

10 

23 
20 
19.5 

16.5 ' 
12.5 

26  ■  ' 
20.25 

10 
6 

19 
19 
30 

15.75 
14.25 

22.75 
24 

*i 

34" 

1 

34  "  " 

*i 

ii" 

■.■■■. 

■■■.: 

16  to  29 
6  to  29 


-10  to  28 
12  to  36 


TABLE  6 

Comparative  Scholarship,  During  Successive   College   Years,   of  Male  Students  Entering 
College  in  1911   at  Different  Ages. 

Scholarship  stated  in  terms  of  numerical  equivalents  of  marks  earned  by  the  median 
student,  the  first  and  third  quartile  student,  and  the  best  and  poorest  students  of  each 
entrance  age  group. 


0  e 


Freshmen 


a  o-d 


Median 
Schol- 
arship 


Range  of 

Middle  50 

percent 


1st 
Quar- 
tile 


3d 
Quar- 
tile 


Range  of 
Scholar- 
ship 
Values 


Sophomores 


a  o-S 
si   - 


Median 
Schol- 
arship 


Range  of 

Middle  50 

percent 


1st 
Quar- 
tile 


3d 
Quar- 
tile 


Range  of 

Scholarships 

Values 


16 

5 

12 

6.5 

25 

17 

17 

17 

10 

21.5 

18 

47 

15 

6 

19 

19 

52 

8.5 

2 

11 

20 

29 

6 

0 

11 

21 

17 

8 

3 

16.5 

22 

5 

20 

1 

24.5 

23 

3 

16 

24 

1 

-2 





25 

1 

-3 

26 

2 

12 

6  to  28 
-4  to  27 
-8  to  28 

-10  to  25 
-10  to  26 
-8  to  24 

-2  to  28 
-8  to  24 


5 
14 
34 

15 

15.5 

15 

7 
12.75 
9 

28.25 
20.25 
24 

31 
19 
10 

11 
8 
7.5 

6 
-2 
3.75 

15 
15 
15.5 

4 

1 

16.5 
25 

-3 

25.25 

1 
1 

16 
11 

.... 

.... 

6  to  29 

9  to  28 

-8  to  37 

-8  to  28 
-8  to  27 
-4  to  26 

-6  to  26 


Juniors 


Seniors 


16 
17 
18 

19 
20 
21 

22 
23 
24 

25 
26 

30 


4 
13 

28 

21.75 
17.25 
20 

12.5* 
14.5 

22  ■  * 
26 

14 
8 
6 

16 

11.5 

15 

13.5 
4.5 
8.5 

18 

9.75 
21.5 

2 

1 

30 
26 



1 
1 

12 
18 

.... 

12  to  28 
6  to  26 
8  to  32 

8  to  37 
0  to22 
4  to  32 

28  to  32 


27 

17.25 

22.5 

21.75 

21 

-1.25 

23.25 
30 


18.5 
13.5 


19 


37 


22.74 
28.5 


30.12 


14.25  to  23.2 
lto37 

18  to  37 
6  to  21 
6  to  17 


60 


THE  SIXTEENTH  YEABBOOK 


TABLE    7 

Comparative  Scholarship,  During  Successive  College  Years,  of  All  Male  Students  Entering 
College  at  Different  Ages. 


Freshmen 


Sophomores 


Median 
Schol- 
arship 


Range  of 

Middle  50 

percent 


1st 

Quar- 

tile 


3d 
Quar- 
tile 


Range  of 
Scholar- 
ship 
Values 


S  OtS 


Median 
Schol- 
arship 


Range  of 

Middle  50 

percent 


1st 

Quar- 

tile 


3d 

Quar- 

tile 


Range  of 

Scholarship 

Values 


16 
17 
18 

8 
29 
77 

14 
16 
14 

8.5 

9 

4.5 

24 
21 
18.5 

19 
20 
21 

95 

58 
24 

9 
5 
8.5 

5 

-1 

6 

14 

11.5 

17.25 

22 
23 
24 

10 
6 

2 

6.5 
16 
12 

2.5 
3.25 

20.25 
23.25 

25 
26 
27 

2 

2 

-4.5 
12 

28 
29 

i 

iV  '  " 

.... 

16 
17 
18 

19 
20 
21 

22 
23 
24 

25 
26 
27 

28 
29 


Juniors 


6  to  28 
-4  to  27 
-8  to  30 

-10  to  25 
-10  to  26 
-8  to  24 

-6  to  28 
-8  to  24 
-2  to  26 

-6  to  -3 


8 
22 
55 

58 
32 
15 


15 
15 
15 

10.5 

8 
8 

13.5 

25 

15 

16 
11 


11 


4.5 
12.75 


8 
2 
5 

3.25 


23.5 

20.25 

21 

16.25 

16 

15 

23.25 


Seniors 


7 
20 
41 

21 
18 
20 

12 

13.25 

14 

28 

20.75 

26 

27 

16 

8 

16 
17 
16 

11 

7.5 
10.5 

23 
24 
19.5 

3 

1 
1 

28 
26 
26 





1 

1 

12 
18 



i 

iV  '  * 

-8  to  29 
6  to  29 
5  to  32 

-4  to  37 
0to35 
4  to  32 

18  to  32 


23 

17.25 

20 

16  '  ' 
17.25 

23  *  ' 
24.37 

21.75 
18 
8 

18.75 

16.5 

2.9 

25 

20.75 

26.8 

23.25 

30 

34 



'.'.'.'. 

18 
13.5 



ii' ' 

3  to  31 
-8  to  28 
-8  to  37 

-8  to  28 
-8  to  29 
-4  to  26 

-6  to  26 


23  to  27 

14  to  29 

lto37 

-10  to  37 
-6  to  36 
-6  to  30 


ENTBANCE  AGE  AS  BELATED  TO  COLLEGE  EFFICIENCY     61 


TABLE  8 

Comparative  Scholarship,  During  Successive  College  Years,  of  Female  Students  Entering 
College  in  1910  at  Different  Ages. 


a  o 

Is 


W 


Freshmen 


^      CD 


Median 
Schol- 
arship 


Range  of 

Middle  50 

percent 


1st 
Quar- 

tile 


3d 

Quar- 

tile 


Range  of 
Scholar- 
ship 
Values 


Sophomores 


Median 
Schol- 
arship 


Range  of 

Middle  50 

percent 


1st 

Quar- 

tile 


3d 

Quar- 

tile 


Range  of 

Scholarship 

Values 


16 
17 

18 

19 
20 
21 

22 
23 

24 

25 
26 

27 

28 
29 
30 

35 


4 
20 
88 

68 
27 
16 

5 

1 
2 

1 
1 


23.5 

16 

15 

13 
11 
17 

13 

20 
18 
15 

16 


11.5 

9 
12 


27.5 
22.5 
20 

18 
17 

22 

24.5 


9  to  28 
-4  to  29 
-4  to  32 

-8  to  31 
-2  to  30 

4  to  26 

5  to  25 
15  to  21 


4 
15 
75 

21.5 

19 

18 

11.75 

12 

14 

30.5 

24 

24 

57 
18 
10 

18 

16.5 

23.5 

13.5 

9.75 
11 

23.5 
22.5 
25.25 

3 

1 
2 

12 
30 
20 



1 
1 

16 
22 

.... 

1 

10 

.... 

1 

6 

10  to  32 
3  to  28 
1  to35 

-4  to  36 

-10  to  30 

7  to  26 

0to27 

14  to  26 


Juniora 


Seniors 


16 
17 

18 

19 
20 
21 

22 
23 
24 

25 
26 
27 

28 
29 


35 


49 
16 


19.5 

18 

21.5 

20 

21.5 

20 

20.5 

23  " 

25 


18.25 

13.5 

15 

16 
14 
19 


32.75 

26 

25 

26 

26.25 

31.5 


18  to  37 
9  to  30 
6  to  34 

0to34 

10  to  32 

8  to  34 

18  to  23 


19 
20 
20 

20 
22 
20 

18 

23" 

28 


17.75 
17 

17 
18 
15.5 


23.5 
22 

24 

24.75 

24 


17  to  22 
15  to  33 
-6  to  29 

8  to  37 
14  to  30 
14  to  27 


62 


THE  SIXTEENTH  YEAEBOOK 


TABLE   9 

Comparative  Scholarship,  During  Successive  College  Years,  of  Female  Students  Entering 
College  in  1911  at  Different  Ages. 


X  u 

ID  -4-3> 


Freshmen 


Median 
Schol- 
arship 


Range  of 

Middle  50 

percent 


1st 

Quar- 

tile 


3d 

Quar- 

tile 


Range  of 

Scholar 

ship 

Values 


Sophomores 


a«t-4     (U 
Ot3 


Median 
Schol- 
arship 


Range  of 

Middle  50 

percent 


1st 

Quar- 

tile 


3d 

Quar- 

tile 


Range  of 

Scholarship 

Values 


16 
17 

18 

19 

20 
21 

22 
23 
24 

25 
26 
27 

28 
29 
30 


2 

22 
94 

76 
39 

10 

5 

1 


6.5 
17 
16 

14 
14 
14 

2 
16 


20 


14 
15 


13.75 
10 


6 
5.5 


20.25 
20.25 

20.75 
18 

18 

16.5 


5  to  8 
-4  to  24 
-6  to  30 

-6  to  27 

-8  to  28 
2  to  20 

-2  to  22 


7  to  33 


2 
20 

74 

51 

27 

1 


7.5 
21 
19 

16 
14 
16 

17 


23 


15 


16.25 
13 


26.75 
23.25 


2  to  13 
5  to  30 
4  to  33 

-8  to  35 
-6  to  40 


10  to  24 


16 
17 
18 

19 

20 
21 

22 
23 
24 

25 
26 
27 

28 
29 
30 


2 
15 
62 

41 
20 

1 


Juniors 


Seniors 


5.12 
22 
20 

19.25 
18.75 
10 


18 


26 


26 
24 


Oto  10 
6  to  30 
6  to  36 

4  to  36 
8  to  26 


12 
54 

31 
15 

1 


19.12 

20.25 

21 

20.25 

15 

19.5 


16.5 


15 


15.5 

18 


17.25 
17.5 


23 
22.69 


24.75 
23.25 


14  to  35 
Oto  36 


11  to  34 
15  to  28 


ENTRANCE  AGE  AS  BELATED  TO  COLLEGE  EFFICIENCY     63 


TABLE    10 

Comparative  Scholarship,  During  Successive  College  Tears,  of  All  Female  Students  Entering 
College  at  Different  Ages. 


16 

17 
18 

19 
20 
21 

22 
63 

24 

25 
26 

27 

28 
29 
30 

35 


Freshmen 


u  to  Median 
^  cl  Schol- 
5*8 -d    arship 


Range  of 

Middle  50 

percent 


1st 

Quar- 

tile 


3d 

Quar- 

tile 


Range  of 
Scholar- 
ship 
Values 


Sophomores 


a  ot3 


S.  Median 
Schol- 
arship 


Range  of 

Middle  50 

percent 


1st 

Quar- 

tile 


3d 

Quar- 

tile 


Range  of 

Scholarship 

Values 


6 

42 
182 

14 
16 
15.5 

7.25 
12.75 
11 

26.5  , 
19.25 
20 

1  144 
66 
26 

13.5 

14 

15 

9 

7 
8 

19 

17.25 

20.25 

10 
2 
2 

8 
18 
18 

1 

22.5 

1 
3 
0 

15 
16 

v.v. 



1 
2 
2 

12 

14 

9 

•  * '  • 

1 

4 

5  to  28  i  6 
-4  to  29  35 
-6  to  32  j  149 

-8  to  31  i  108 
-8  to  28  I  45 
2  to  26  1     11 


-2  to  25 
16  to  20 
15  to  21 

15 
7  to  33 


12 
3  to  25 
3  to  15 


15 
21 
18 

17 
15 
23 

12 
30 
20 

16 
22.5 


10 

io.V 


27.5 

26 

23 

20.75 

22 

24 

25.5 


2  to  32 

3  to  30 
lto35 

8  to  36 

-10  to  40 

7  to  26 

0  to  27 

30 

14  to  26 

16 
22  to  23 


10 

6  to  is 


16 
17 

18 

19 
20 
21 

22 
23 
24 

25 
26 
27 

28 
29 
30 

35 


Juniors 


Seniors 


6 

27 
126 

18.5 

21 

20 

7.69 
15 
16 

24.25 

2G 

24.25 

90 
36 

10 

19.37 
19.5 

20 

16 
14 
17.5 

26 
24 
30.25 

3 
0 

1 

23 
23  '  ■ 



1 
1 
0 

25 
18 



0 
0 

1 

26  "  * 



0 

.... 

Oto37 
6  to  30 
6  to  36 

0  to  36 
8  to  33 
8  to  34 

18  to  24 

'"23" 

25 

18 


26 


4 

22 
108 

73 
31 


18.5 
19.75 

20 

20.25 

21 

18.5 

18.75 

23" 

28 
16.5 


22.5 


17.25 
17.19 
17.25 

17 

18 

14.75 


21.25 
23.06 
22 

24 

24 

22.5 


17  to  22 
13.75  to  35.50 

-6  to  36.75 

8  to  87 
14  to  30 
14  to  27 

18  to  19.5 

* '23' " 

28 
16.5 


22.5 


64 


TEE  SIXTEENTH  YEABBOOK 


TABLE  11 

Number  of  Semesters  Spent  in  College  by  the  Median  Student,  the  First  and 

Third  Quartile  Students,  and  the  Two  Extreme  Students  of  Each 

Age-Group.     Males  Entering  in  1910. 


Age  at 
Entrance 

Number 
of 

Students 

Median 
Semester 
Eetention 

Middle  50  Percent       | 

Range  of 

1st 
Quartile 

3d 
Quartile 

Semester 
Retention 

16 
17 
18 

3 
12 
30 

8 
5.75 

4 

2 
2 

*8 
8 

5  to  8 
2  to  8 
1  to  8 

19 
20 
21 

43 

4 

2 
4 

2 

1 
2 

6 
5 
5 

1  to  8 

1  to  8 

2  to  8 

22 
23 
24 

5 
3 
1 

1 

1 

4.5 

1  to  5 

2  to  2 

25 
26 
27 

1 

1 

•• 

•• 

28 
29 

"i 

8 

•• 

•• 

TABLE  12 

Number  of  Semesters  Spent  in  College  by  the  Median  Student,  etc. 

Entering  in  1911. 


Males 


Age  at 
Entrance 

Number 
of 

Students 

Median 
Semester 
Retention 

Middle  50  Percent 

Range  of 

1st 
Quartile 

3d 
Quartile 

Semester 
Retention 

15 
16 
17 

5 
17 

5.75 
5.75 

3.25 
5.38 

6 
8 

3  to  6 
1  to  8 

18 
19 
20 

47 
52 
29 

5.5 

3 

3 

2 
2 
2 

8 

5.5 

5.5 

1  to  10 
1  to  8 
1  to  10 

21 
22 
23 

17 
5 
3 

3 
3 

1 

2 
2.5 

5.5 
6.75 

1  to  8 

2  to  8 
1  to  8 

24 
25 
26 

1 
1 
2 

1 

8 
5 

•• 

•• 

1 

8 

1  to  8 

No  entrants  older  than  26  in  this  class. 


ENTRANCE  AGE  AS  BELATED  TO  COLLEGE  EFFICIENCY        65 

TABLE  13 

Number  of  Semesters  Spent  in  College  by  the  Median  Student,  etc.  All  Males. 


Age  at 
Entrance 


Number 

of 
Students 


Median 
Semester 
Eetention 


Middle  50  Percent 


1st 
Quartile 


3d 
Quartile 


Range  of 
Semester 
Retention 


16 

8 

6 

5.5 

6.25 

1  to  8 

17 

29 

5.75 

2.25 

8 

1  to  8 

18 

77 

5.5 

2 

8 

1  to  10 

19 

95 

3 

2 

5.5 

1  to  8 

20 

58 

3 

2 

5.5 

1  to  10 

21 

24 

3.5 

2 

5.5 

1  to  10 

22 

10 

3 

1 

5.5 

1  to  8 

23 

6 

2 

1 

3.5 

1  to  8 

24 

2 

4.5 

.. 

.. 

1  to  8 

25 

2 

5.5 

1  to  10 

26 

2 

5 

. , 

. . 

2  to  8 

27 

•• 

•• 

•• 

•• 

•• 

28 

29 

1 

8 

8 

30 

TABLE  14 

Number  of  Semesters  Spent  in  College  by  the  Median  Student,  etc.    Females 

Entering  in  1910 


Age  at 
Entrance 

Number 

of 
Students 

Median 
Semester 
Retention 

Middle  50  Percent 

Range  of 

1st 
Quartile 

3d 
Quartile 

Semester 
Retention 

16 
17 
18 

4 
20 
88 

8 

6.25 

8 

5.75 

2.5 

4 

8 
8 
8 

5  to  8 
1  to  8 
1  to  8 

19 
20 
21 

68 
27 
16 

8 
8 
5 

4 
2 
2 

8 
8 
8 

1  to  8 
1  to  8 
1  to  8 

22 
23 
24 

5 

1 
2 

4 
3 
6 

2 

7 

2  to  8 

3 
4  to  8 

25 
26 
27 

1 
1 
0 

8 
4 

•• 

•• 

•• 

28 
29 
30 

1 
0 

1 

4 

•• 

•• 

•• 

35 

1 

2 

.. 

.. 

.. 

66 


TEE  SIXTEENTH  YEAEBOOK 


TABLE  15 

Number  of  Semesters  Spent  in  College  by  the  Median  Student,  etc. 

Entering  in  1911. 


Females 


Age  at 
Entrance 

Number 

of 
Students 

Median 
Semester 
Ketention 

Middle  50  Percent 

Range  of 

1st 
Quartile 

3d 
Quartile 

Semester 
Retention 

16 
17 
18 

19 

20 
21 

22 
23 
24 

25 
26 
27 

28 
29 

30 

2 
22 
94 

76 
39 
10 

5 
1 

*2 

'2 

1 

5.5 

8 
8 

5.5 

5.5 
2 

1 
1 

6* 

2" 

8 

'4 
3 

2 
2 
1.75 

1 

's 

8 

8 
8 
2 

6 

5  to  6 
1  to  10 
1  to  10 

1  to  10 
1  to  8 
1  to  8 

1  to  8 

1 

2  to'  10 

'2 

8 

TABLE  16 

Number  of  Semesters  Spent  in  College  by  the  Median  Student,  etc.  All  Females. 


Age  at 
Entrance 

Number 

of 
Students 

Median 
Semester 
Retention 

Middle  50  Percent 

Range  of 

1st 
Quartile 

3d 
Quartile 

Semester 
Retention 

16 
17 
18 

6 

42 

182 

7.75 
7.75 
8 

5.25 

4 

4 

8 
8 
8 

5  to  8 
1  to  10 
1  to  10 

19 

20 
21 

144 
66 
26 

6.5 
5.5 
2 

2.5 

2 

2 

8 

8 

7 

1  to  10 
1  to  8 
1  to  8 

22 
23 
24 

10 
2 

2 

3 
2 

6 

1 

6.5 

1  to  8 
1  to  3 

4  to  8 

25 
26 
27 

1 
3 
0 

8 
4 

8 
2  to  10 

28 
29 
30 

1 

2 
2 

4 

2 
5.5 

4 

2 

3  to  8 

35 

1 

2 

2 

ENTRANCE  AGE  AS  BELATED  TO  COLLEGE  EFFICIENCY 


9^ 

31 

9<f 

19 

> 

U 

-^ 

y 

V: 

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-W- 

<^^ 

-^-> 

' 

<-*' 

U 

- 

•— <J^  — 

- 

19 
If 

-^ 

\  \v 

n 

Males 

-^>^- 

th 

[^K. 

- 

-J 

3         a-        1 

o           ,3-         Z 

o        ztr      oo 

75 

30 
x.e 

X6 

i" 

i4  25 


\ 

V 

X    ^ 

^' 

'V      \ 

"^"^ 

'^'1 

- 

- 

4" 

Fcmoici 

."* 

-i-.  — 

^     i     *■      » 

0       ly      A      7.S-     3o 

AVe^oa  i3cfaclar»k<p  Vahtt  Total 

Closi  I'. 


A^edion  Sokolarjhi^  Values 


Class  l9/(-lz 

GRAPH  II. 

Comparative  Scholarship  During  Freshman  Year  of  Students  Entering 
College  at  Different  Ages. 
The  horizontal  broken  lines  indicate  the  range  of  each  ' '  middle  50  percent. ' ' 


33 

31 

\           \ 

\ 

\ 

\ 

IS 

^ 

s. 

0 

< 

*i 

..— 4- 

:^ 

z\ 

20 
16 



"^^ 

. 

> 

»7 

16 

■A 

^ 

-5         c 

3-           , 

o      ,r      £ 

9         A«^        O 

GRAPH  III 

Comparative  Scholarship  During  Sophomore  Year  of  Students  Entering 

College  at  Different  Ages. 

The  horizontal  broken  lines  indicate  the  range  of  each  ' '  middle  50  percent. ' ' 


68 


THE  SIXTEENTH  YEABBOOK 


^3 
JZ. 
31 

50 
t9 
U 

c 

in 

ii 

Z.0 
19 

\ 

\ 

< 

/ 

jk 

<it 

:i> 

n 

lb 

nalps 

:' 

^ 

J          ^        • 

/^e^ian'  Scholarship    Valup^ 


J-        »o         »^        zo 
^€^tan  Scho\ar9hip    >/ci\ae'6 


GRAPH  IV. 

Comparative    Scholarship   During   Junior   Year   of    Students   Entering 

College  at  Different  Ages. 

The  horizontal  broken  lines  indicate  the  range  of  each  * '  middle  50  percent. ' ' 


33 
3Z 

•>i 

30 

X8 
*7 

r 

Zo 
19 


%- 

V 

=- 

\ 

Atof^S 

^ 

'tlIZ4 

zx 

3A 
19 
18 
•  7 
|6 


^- 

// 

^ 

^ 

4 

/ 

^-^ 

\ 

F 

T>=mc 

■ — S" — ^ 

Al^<li<aa.   Schol  arsbip  Vofi^s  /ied»aa  Solu)larsKip    Vofwc* 

GRAPH  V. 

Comparative    Scholarship   During    Senior   Year  of   Students    Entering 

College  at  Different  Ages. 

The  horizontal  broken  lines  indicate  the  range  of  each  ' '  middle  50  percent. '  ^ 


ENTBANCE  AGE  AS  BELATED  TO  COLLEGE  EFFICIENCY 


GEAPHVI. 

Comparative  Scholarship  During  Successive  College  Years  op  Students 
Entering  College  at  Different  Ages. 


DIFFERENCES  APPEARING  DURING  SUCCEEDING  COLLEGE  YEARS 

1.  In  both  sexes  the  depression  representing  the  intermediate 
ages  from  19  to  21  or  22  decreases  in  passing  from  the  freshman  to 
the  senior  year,  and  practically  disappears  by  the  time  the  latter 
year  is  reached ;  the  males  who  entered  at  21  and  the  females  who 
entered  at  21  and  22,  alone  still  show  some  deficiency  in  the  senior 
year. 

2.  There  is  an  increase  in  the  standard  of  scholarship  shown 
by  all  entrance  groups  np  to  the  junior  year,  but  little  increase  is 
noticeable  between  the  junior  and  the  senior  years. 

3.  This  increase  in  standard  of  scholarship  from  year  to  year 


70  THE  SIXTEENTH  YEABBOOK 

is  more  marked  among  the  older  than  among  the  younger  entrants, 
in  both  sexes,  but  particularly  in  the  males. 

All  three  of  the  changes  described  as  occurring  from  year  to 
year  are  closely  connected  with  the  elimination  phenomena  to  be 
outlined  in  the  next  section.  A  discussion  of  these  changes,  inde- 
pendent of  the  elimination  factor,  will  appear  in  the  next  chapter, 
where  the  record  of  those  students  who  remained  for  four  full  years 
is  separately  described. 

Section  2 

relation  between  entrance  ages  and  college  efficiency  as 
displayed  by  elimination  and  retention 

The  relation  between  annual  entrance  age  and  retention  in  col- 
lege is  important  for  two  reasons ;  first,  it  furnishes  another  criterion 
of  college  efficiency ;  and  second,  it  affords  a  means  of  explaining,  at 
least  in  part,  the  increase  in  standards  of  scholarship  which  we  have 
found  appearing  in  successive  college  years. 

We  shall  attempt  to  demonstrate  this  relationship,  first,  in 
terms  of  the  number  of  semesters  which  the  median  student  of  each 
age-group  remained  in  college ;  and  second,  in  terms  of  the  percent 
dropped  from  each  age-group  during  or  at  the  end  of  each  college 
year. 

1.  Retention  described  in  terms  of  semester  retention  of 
median  pupil.  The  tables  and  graph  here  presented  (Tables  11  to  16, 
and  Graph  VII),  resemble,  in  form,  those  of  the  preceding  section. 
The  semester  retention  of  each  age-group  is  stated  in  terms  of 
(1)  the  extreme  range,  (2)  the  range  of  the  middle  50  percent,  and 
(3)  the  median.  The  sole  difference  is  that  here  are  portrayed  the 
number  of  semesters  spent  in  college  by  the  median,  the  first  and 
third  quartile,  and  the  two  extreme  students  of  each  age-group  that 
is  represented,  rather  than  their  marks. 

Reference  to  the  ''total"  curves  in  Graph  VII  reveals  the  fol- 
lowing facts : 

a.  The  retention  curves,  like  the  mark  curves,  are  bi-modal. 
Again  the  central  depression  (or  bend  toward  the  abscissa)  begins 
with  the  entrance  age  of  19,  but  here  extends  to  include  the  22-year- 
old  entrance  group. 


ENTRANCE  AGE  AS  BELATED  TO  COLLEGE  EFFICIENCY        71 

b.  The  superiority  of  the  older  entrants  (above  23)  in  reten- 
tion is  more  marked  and  more  consistent  than  their  superiority  in 
scholarship. 

c.  The  middle  50  percent  shows  a  change  in  position  with 
the  different  entrance  ages  which  fairly  parallels  the  changes  shown 
by  the  medians. 

2.  Retention  described  in  terms  of  percentages  eliminated 
annually.  Tables  17  and  18,  with  Graphs  VIII  and  IX,  state  the 
percentages  of  the  two  entrance  classes  combined  who  were  elim- 
inated during,  or  at  the  end  of,  the  freshman,  sophomore,  and  junior 
college  years.  Senior  eliminations  were  too  few  to  be  considered  in 
terms  of  annual  entrance  ages.  An  attempt  is  also  made  in  these 
tables  and  graphs  to  evaluate  two  important  causes  of  elimination ; 
i.  e.,  poor  scholarship  and  change  in  college  plans. 


«9 

> 

<.c 

'^] 

-.-- 

'rX"" 

*Cr-rr  — 



n 



V 

-v"; 

1 

■i      1 

5 

7             S 

s|Totei  '        z        :>       -f        y       (,        7 

|Cia3siiii.iA— > 

GRAPH  VII. 

Comparative  Retention  of  Students  Entering  College  at  Different  Ages, 
Stated  in  Terms  of  the  Number  of  Semesters  Which  the  Median 

Student  of  Each  Entrance-age  Group  Remained  in  College. 
(The    horizontal  broken  lines    indicate  the   range    of   the   "middle    50 

percent. '0 


72 


TEE  SIXTEENTH  TEAEBOOE 


The  University  of  Minnesota  has  had  a  ruling  to  the  effect 
that  any  student  who  stood  below  passing  grade  in  three  or  more 
subjects  should  be  dropped.  To  the  students  leaving  college  under 
these  conditions,  we  have  added  those  who  received  a  C  or  an  F 
in  all  of  their  work  in  case  they  were  carrying  fewer  than  three 
subjects.  These  students  we  have  regarded  as  eliminated  clearly 
because  of  poor  scholarship,  and  have  so  entered  them  in  the  tables 
and  graphs.  It  is  highly  probable  that,  through  discouragement, 
poor  scholarship  caused  the  elmination  of  many  others,  but  tne 
extent  of  this  influence  cannot  be  measured.  Certainly,  we  remain 
well  within  the  truth  when  we  confine  our  tables  to  those  cases  in 
which  the  university  could  take  action. 


■Pfr.sbr>»p". 

so 

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1 

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551 1 

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n 

m^^^^i^ 

^^^ 

HSSI-    -I 

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D 

16 

So     4o     te 

c--fco       ?c    ' 

6b— 5V-;^ 

■Sopho'W-oriZ.a 


Jorviors 

SO 

ze 

^  =^ 

I:: 

1 

ZD 

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/o      Ax> 

JO    -,o     Jr 

o       to      7P 

So     9a    «o. 

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io        JO     5o     ffo     So     -Vo '    eo 


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3o 

ze 

Z7 

Z.5 
2.+ 

, 

1 

^^^^^^^H 

X-Z, 

19 

HBM 

— 1 

18 

{■NNS 

1 

»o       io 

50       <»o      S 

o      feo      7o 

80       9o    1 

'^C'rcc.n.faqp  X,J(f»(nof<d 


GEAPH  VIII. 


Comparative  Elimination,  with   Principal  Causes,   of  Males   Entering 
College  at  Different  Entrance-Ages. 


ENTRANCE  AGE  AS  BELATED  TO  COLLEGE  EFFICIENCY       73 


o 


OS 

I 

as 

1 
■3 

Cause 
Un- 
known 

q  q  q 

d  CO  00 
10  r-l  ©q 

CO  ic  iq 
10  »•'  t>3 

Tji  CO  CO 

0  t-    . 

.  q    . 

'  d    * 
in 

To 
Enter 
Other 
De- 
part- 
ments 

•  CO  TiJ 
(M  r-l 

rH  Tt|  !>. 

co'  d  d 

r-H  1— ( 

0  •  • 

d    *    • 

rH 

:  :  : 

For 
Poor 
Schol- 
arship 

10  00   TJJ 
C<J  d  CO 
rH  Oq  (M 

in  »n  (?q 

rH  d  d 

CO  ■*  CO 

0  t^  0 

d  d  d 

50.0 

Total 
Per- 
cent 
Elimi- 
nated 

10  0  '<*< 

(m"  (m*  (^i 

<x>  CO  «:> 

Ci  >n  -^ 

d  rj?  co' 

t^  00  00 

Q  •>:  0 

d  CO  d 
ci  GO  in 

0  0    • 
d  d    • 
in  in 

1 

•-3 

Cause 
Un- 
known 

10  CO  00 
t^  CO*  t>-' 

CO  iH 

oq  00  t^ 
c<i*  th  d 

I— 1 

q    .    . 
d    *    * 

To 
Enter 
Other 
De- 
part- 
ments 

•  00  10 

•  co'  d 

T— t 

r-J  q     . 

co'  d    • 

q    .     . 

r-i       ■       ' 

For 
Poor 
Schol- 
arship 

10  10  CO 
C<j  CO*  r-i 

CO*  co'    • 

:  :  : 

Total 
Per- 
cent 
Elimi- 
nated 

0  0  «o 

d  T-H  LO 

10  CO  T-l 

TjJ  iH  !>. 

00*  cq  d 

r-H  r-l 

20.0 

•1 

.3 
2 

i 

Cause 
Un- 
known 

12.5 
9.1 

rH  -^^  in 

co'  d  cq* 

Oq  rH  r-( 

0  •  • 

d    •     • 

cq 

To 
Enter 
Other 
De- 
part- 
ments 

•  10  CO 

•  co'  oq 

•  rH  cq 

•  in  -* 

:  :  : 

For 
Poor 
Schol- 
arship 

.  10  10 

:  co'  d 

in  rH  10 

d  cq  cq' 

rH  r-i 

q     .     . 

d    *    ' 

Total 
Per- 
cent 
Elimi- 
nated 

»o  Oi  cq 
co'  d  oo" 

CD  CO  cq 
cq'  b-*  d 

CO  cq  cq 

q    .    . 

d    '    • 
CO 

1 

.S 

a 
i 
i 

1 

Cause 
Un- 
known 

'  d  th 

r-i  1-1 

q  "^^  CO 
d  d  00* 

eg  r-t 

10.0 
66.7 

.  q    . 

•  d    • 
in 

To 
For    Enter 
Poor    Other 
Schol-    De- 
arship    part- 
ments 

•       •  CO 
'      '  rA 

•  eo'  oi 

r-i 

'.    '.    ' 

.  00  CO 

•co'  16 

iH  r-i 

C5  0  t- 
00'  r-i  d 
rH  CO  rH 

0  t-  0 
d  d  d 

CO  rH  in 

0    •    • 
d    •    • 
in 

Total 
Per- 
cent 
Elimi- 
nated 

.  rH  CO 
•  tH  06 

(M  oq 

Cioo  in 
00'  Tji  t>: 

CO  T*H  CO 

0  CO  0 

d  co'  d 
TtH  CO  m 

50.0 
50.0 

Num- 
ber 
of  Stu- 
dents 

*^^ 

in  00  T}i 
05  m  (M 

0  CO  cq 

rH 

cq  CQ    . 

•  i-\    ' 

Age 
at  En- 
trance 

5?^S 

Oi  0  rH 

rHcq  cq 

cq  CO  T« 
cq  cq  cq 

in  CD  t- 
eg  cq  cq 

00  CJ>  0 
cq  cq  so 

74 


TEE  SIXTEENTH  YEARBOOK 


N 


a 

rse 

■o 

!r( 

oo 

r-l 

Kl 

H^ 

•i 

1-1 

3 

H 

s 

fe^ 


1 

1 

3 

o 

Cause 
Un- 
known 

t>.  iq  G<i 

d  d  d 

tH  'TiH  CO 

kO  00  t>. 

t-*  rH  (>.* 

CO  CO  lo 

q  q  q 
d  d  d 

TJH    O    lO 

•  b-    . 

•  d    • 

CO 

o  o  o 

d  d  d 
o  »o  »o 

o 
d 
o 

To 
Enter 
Other 
De- 
part- 
ments 

.      .  CO 
*      *  i-H 

:  :  : 

:  :  : 

:  :  : 

For 
Poor 
Schol- 
arship 

t-  tH  00 

d  t-'  00 

T— 1 

10.4 
19.6 
19.2 

40.0 

:  :  : 

.  o      • 

•  d    ■ 

LO 

Total 
Per- 
cent 
Elimi- 
nated 

CO  O  CO 

CO  t-*  d 

CO  '-^  ■'+1 

CO  OS  05 

d  oci  d 

Tji  lO   t^ 

o  o  <p 
d  d  d 

GO  O  lO 
rH 

•  d     • 
o 

Q  O  cp 

O 
rH 

o 

V 

^-5 

Cause 
Un- 
known 

•^  Oi  Oi 

d  rA  oi 

T— 1    1— 1 

tH  rH  tH 
rH*  d  lO 

o    •    . 

d    •    • 

rH 

:  :  : 

:  :  : 

To 

Enter 
Other 
De- 
part- 
ments 

* 

.  . 

... 

Total  For 
Per-  Poor 
cent     Schol- 

Elimi-  arship 

nated  I 

d    •    • 

:  :  : 

:  :  : 

:  :  : 

CO  Oi  05 

CO"   rH   oi 
CO  r-i 

00  q  -^^ 

rH  t-'  LO 

T-i               T-\ 

q    .     . 
d    '    • 

r-l 

:  :  : 

:  :  : 

o 

o 

Pu 
o 

Cause 
Un- 
known 

•  d  d 

i-H   I— 1 

O    O          • 

d  d    • 

q  q  o 
d  d  d 

CJ  LO  LO 

.  CO      • 

■  co'    ■ 

CO 

50.0 
50;0 

To 
Enter 
Other 
De- 
part- 
ments 

•      •  LO             ... 

■    •  d 

For 
Poor 
Schol- 
arship 

IC  LO  00 
Tl^  TtH  CO 

:  :  : 

:  :  : 

:  :  : 

• 

Total 
Per- 
cent 
Elimi- 
nated 

.  q  o 
■  d  c4 

lO  iO  00 

CQ  Co'  CO 

o  o  o 
d  d  d 

<M  LO  LO 

•CO       • 

•  co'     ' 

CO 

50.0 
50.0 

: 

i 

i 

Cause 
Un- 
known 

■  d  d 

q  b^  CO 
d  d  cm' 

rH  rH  Tfl 

o  o     • 

d  d    • 

rH  LO 

.  CO       • 

'  co"     * 

CO 

•  d    • 

o 
d 
o 

rH 

To 
Enter 
Other 
De- 
part- 
ments 

rH  rH      * 

:  :  : 

:  :  : 

:  :  : 

• 

For 
Poor 
Schol- 
arship 

q  q  Tj^ 

l>^  co'  LO 

rH   tH 

q     .     . 

d     ■     * 

:  :  : 

.  o    . 

•  d    • 

uo 

; 

Total 
Per- 
cent 
Elimi- 
nated 

•  d  GO* 

1-H   I-H 

O  QO  t- 

LO  ^  t^ 

(M  CO  LO 

o  o    • 

d  d     * 

lO  iO 

•  CO     • 

'  co'     ■ 

CO 

.  o    . 

y—i 

q 

Num- 
ber 
of  Stu- 
dents 

CO  01  CM 

TfH   CX) 

I— 1 

tJH  CD  O 
Tj.  O  (M 

o  cq  oci 

r-{  CO       • 

rH  <M  03 

»H 

Age 
at  En- 
trance 

o  t-  00 

O:  O  rH 
rH  (M  CM 

<M  CO  Ttl 

(M  oq  (M 

LO  CO  b- 

oq  eg  (M 

00  Oi  O 

(M  cq  CO 

CO 

ENTRANCE  AGE  AS  BELATED  TO  COLLEGE  EFFICIENCY 


75 


^rcshm 

cn. 

30 

5'- 



17 
16 

=1 

■■ 

'-    .0    '   io 

3C     *o     S 

6    60     70 

eo     90    .0 

Jt/onor» 


00      ♦O       iO      6O       70 


ftiWurf 


OHi«rCoJlM>A 


C   26 


Joph-c 


o    4o     gi>     60      ^6       ^_ 


?6''c«.ata9^  £:,/<mioofM 


GRAPH  IX. 


Comparative  Elimination,  with  Principal  Causes,  of  Females  Entering 
College  at  Different  Ages. 

In  the  columns  headed  * '  Other  Departments ' '  we  have  included 
those  who  left  the  College  of  Arts  and  Sciences  to  enter  some  other 
college  department  of  the  University  of  Minnesota.^  Changes  to 
other  colleges  outside  the  university  are  not  recorded ;  there  are  no 
data  available  upon  that  subject. 

The  material  contained  in  the  tables  is  fully  represented  in  the 
graphs.  We  may  consequently  base  our  inferences  upon  the  latter 
alone. 


-These  "other  departments''  include  the  Colleges  of  Law,  Medicine, 
Dentistry,  Pharmacy,  Engineering,  and  Agriculture.  Students  transferring  to 
the  College  of  Education  were  treated  as  continuing  in  the  College  of  Arts, 
because  the  greater  part  of  their  work  was  still  in  the  latter  college.  The  caption 
"other  departments"  is  used  in  preference  to  "other  colleges,"  to  avoid  con- 
fusion of  these  students  with  those  who  left  the  University  of  Minnesota  to 
enter  college  elsewhere. 


76  THE  SIXTEENTH  YEABBOOK 

1.  In  both  sexes  the  elimination  occurs  mostly  during  the 
freshman  year,  and  least  during  the  junior  year. 

2.  During  the  freshman  and  sophomore  years,  in  both  sexes, 
elimination  increases  generally  with  increase  in  entrance  age.  In 
the  junior  year,  this  tendency  appears  to  be  reversed. 

3  Inspection  of  the  ''total"  section  of  each  graph  shows  that, 
in  both  sexes,  elimination  is  greater  from  ages  19  to  23,  inclusive, 
than  from  ages  16  to  18,  or  24  to  26.  The  graph  for  females  shows 
another  increase  in  the  more  advanced  entrance  ages,  but  the  cases 
here  are  few  in  number. 

4.  Both  causes  of  elimination  noted,  poor  scholarship  and 
change  from  one  department  to  another,  are  more  effective  among 
the  males  than  among  the  females. 

5.  Among  the  males,  poor  scholarship  is  far  more  effective 
during  the  freshman  year,  and  change  of  department  is  somewhat 
more  important  during  the  junior  year.  Both  causes  display  their 
greatest  influence  upon  the  females  during  the  freshman  year. 

6.  Poor  scholarship  eliminations  show  a  general  tendency  to 
increase  with  entrance-age  up  to  the  25-year-old  male  entrants  and 
the  22-year-old  female  entrants. 

Section  3 

SUMMARY 

The  foregoing  facts  demonstrate  the  existence  of  certain  rela- 
tions between  the  ages  at  which  these  students  entered  college  and 
the  quality  and  consistency  of  their  college  work. 

The  point  to  which  we  would  call  particular  attention  is  the 
clear  inferiority,  at  least  during  the  freshman  year,  of  what  we  may 
call  the  middle  entrance  ages,  most  marked  from  20  to  22.  This 
inferiority  is  evident  both  in  scholarship  and  in  retention.  The 
students  who  entered  college  after  19  and  before  23  or  24,  therefore, 
showed  inferior  efficiency,  as  compared  with  those  who  entered 
younger.  The  students  who  entered  after  the  ages  of  23  or  24  are 
too  few  in  number  to  be  very  dependable,  but  there  would  appear 


ENTRANCE  AGE  AS  BELATED  TO  COLLEGE  EFFICIENCY       77 

to  have  been  some  improvement  in  their  eases.  The  differences  men- 
tioned, particularly  the  scholarship  differences,  are  more  conspic- 
uous among  the  males  than  among  the  females. 

In  passing  from  the  freshman  to  the  senior  college  year,  the 
groups  which  showed  marked  deficiency  during  the  freshman  year 
practically  overtook  the  other  groups.  One  cause  of  tills  pnenom- 
enon  is  very  clear ;  i.  e.,  that  there  was  a  greater  proportional  elimin- 
ation of  poor  students  from  these  middle-age  groups  during  the  early 
college  years.  In  a  later  chapter,  we  shall  present  what  is  at  least 
a  partial  explanation  of  all  of  the  phenomena  which  we  have  just 
described. 

The  preceding  study  of  the  individual  entrance  ages  suggests 
the  feasibility  of  combining  these  ages  for  further  treatment  into 
three  groups,  which  we  may  call  the  normal,  the  pre-normal,  and 
the  post-normal  entrance-ages.  A  discussion  of  the  college  efficiency 
of  the  students  making  up  each  of  these  three  groups  follows  in  the 
next  chapter. 


CHAPTER  V 

NORMAL,  PRE-NORMAL,  AND  POST-NORMAL  ENTRANCE 
AGES  AS  RELATED  TO  COLLEGE  EFFICIENCY. 

This  chapter  aims  to  contrast  the  efficiency  shown  by  those 
students  who  entered  college  at  what  may  be  deemed  a  normal 
entrance  age,  with  that  of  those  who  entered  before  or  after  normal 
age. 

Our  first  problem  is  to  determine  what  may  be  regarded  as  the 
normal  age  or  ages  at  which  students  should  enter  college.  This  we 
may  arrive  at,  first,  as  follows :  In  an  earlier  chapter  we  have  noted 
that  the  most  auspicious  age  for  entrance  into  the  elementary  school 
seems  to  be  six.^  It  is  contended  by  many  authorities  that  normal 
progress  through  the  grades  should  be  based  upon  entrance  at 
the  age  of  six,  plus  one  year  to  allow  for  the  frequent  repetition  of 
the  first  grade.2  Adding  twelve  years,  the  length  of  the  stand- 
ard American  pre-coUegiate  course,  to  six  years,  the  normal  age  for 
entering  the  elementary  school,  gives  eighteen  as  the  normal  age 
for  entrance  at  college,  irrespective  of  sex.  Allowance  for  the  year 
of  leeway  recommended  by  many  writers,  would  extend  this  normal 
entrance  period  to  include  nineteen.  Eighteen  and  nineteen  thus 
become  the  normal  ages  for  college  entrance.  This  idea  is  confirmed 
by  King's  statement  that  60  percent  of  our  pupils  enter  the  high 
school  at  fourteen  and  fifteen,  and  that  there  is  little  difference 
between  the  sexes  in  this  regard.^ 

The  conclusion  may  be  confirmed  thus:  The  percentages  of 
college  students  who  entered  at  different  ages,  as  found  in  the 
present  study,  have  already  been  presented  in  Table  4.  In  this 
table  we  find  that  fully  60  percent  of  the  students  of  both  sexeu* 
entered  at  the  ages  of  eighteen  and  nineteen,  and  that  more  students 


^See  Chapter  II,  Section  1. 

^Van  Sickle,  Witmer,  and  Ayres.     Provision  for  Exceptional  Children  in 
Tublic  Schools.    Bulletin  U.  S.  Bureau  of  Education,  1911.     No.  14. 
^King,  Irving.    The  High  School  Age.    Bobbs-Merrill,  1914,  p.  187. 

78 


NORMAL,  PBE-NOBMAL,  POJST-NOBMAL  ENTBANCE  AGES       79 

of  each  sex  entered  at  either  of  these  ages  than  entered  at  any  other 
one  age.  If  the  comparative  number  of  entries,  therefore,  can  be 
taken  to  indicate  the  normal  time  for  entering  college,  then  ages 
eighteen  and  nineteen  are  again  shown  to  be  the  normal  ages  for 
entrance,  while  ages  preceding  these  may  be  regarded  as  pre-normal, 
and  ages  following  them  as  post-normal.  A  comparison  of  the  effi- 
ciency of  the  students  who  entered  before  18,  at  18  and  19,  and  after 
19  years  of  age,  constituting  respectively  our  pre-normal,  normal, 
and  post-normal  entrance  groups,  becomes  the  problem  of  this 
chapter. 

Section  1 

comparative  college  efficiency  as  measured  by 
scholarship  marks 

The  tables  and  graphs  accompanying  this  section  are  similar  in 
form  and  interpretation  to  those  in  Section  1  of  Chapter  IV.  There 
are  but  two  differences.  First,  we  consider  here  only  three  entrance 
groups,  each  a  combination  of  several  of  the  age-  groups  discussed 
in  the  previous  chapter.  Secondly,  we  discontinue  separate  treat- 
ment of  the  classes  entering  in  1910  and  1911.  In  this  chapter,  and 
henceforth  throughout  the  study,  we  shall  treat  these  classes  as  if 
they  formed  a  single  entering  class,  in  order  to  simplify  our  pre- 
sentation and  to  deal  with  the  largest  possible  numbers.  The 
author,  however,  has  carried  through  the  study  for  each  class  sep- 
arately, and  has  found  that  each  class  alone  displays  the  same 
general  tendencies  shown  by  the  combined  classes. 

The  reader's  attention  is  first  directed  to  Table  19,  illustrated 
by  Graph  X.  Table  19  shows  the  comparative  scholastic  efficiency, 
measured  by  the  total  mark  values  used  in  the  preceding  chapter, 
of  the  males  and  females  entering  at,  before  and  after  normal 
entrance-age.  The  scholarship  of  each  group  is  displayed  in  terms 
of  (1)  the  median  student,  (2)  the  first-  and  third-quartile  students, 
and  (3)  the  total  range  between  the  best  and  poorest  student  in  each 
series.  Comparisons  are  made  separately  for  each  of  the  four  college 
years.  Graph  X  illustrates  the  columns  entitled  ' '  Median  Scholar- 
ship" in  the  table,  with  lines  of  different  character  indicating  the 


80 


THE  SIXTEENTH  YEABBOOK 


TABLE    19 

The  Comparative  Scholarship  Values,  in  Terms  of  the  Median,  Middle  50  Percent  and 
Total  Range,  of  Students  Entering  College  at,  before,  and  after  Normal  Age. 


Age  at 
Entrance 


Males 


Median 
Schol- 
arship 


Middle  50 
percent 


1st 

Quar- 

tile 


3d 

Quar- 

tile 


Range  of 

Scholarship 

Values 


Females 


Median 
Schol- 
arship 


Middle  50 
percent 


1st 

Quar- 

tile 


3d 

Quar- 

tile 


Range  of 

Scholarship 

Values 


Freshmen 

Freshmen 

Pre- 

Normal 

37 

16 

9 

21 

-4  to  28 

48 

16 

11.25 

19.75 

-4  to  29 

Normal 

172 

10 

5 

17 

-10  to  30 

326 

15 

10 

20 

-8  to  32 

Post- 

Normal 

105 

8 

0 

15 

-10  to  28 

116 

14 

7 

18 

-8  to  33 

Sophomores 

Sophomores 

Pre- 

Normal 

30 

15 

10.75 

21.75 

-8  to  31 

41 

21 

15 

26 

2  to  32 

Normal 

113 

14 

8 

19 

-8  to  37 

257 

17 

13 

23 

-6  to  36 

Post- 

Normal 

57 

9 

4.5 

16 

-8  to  29 

70 

16 

11.5 

24 

-10  to  40 

Juniors 

Juniors 

Pre- 

Normal 

27 

18 

13            22 

-8  to  29 

33 

20 

16 

26 

0to37 

Normal 

68 

18 

14            25.75 

-4  to  36 

216 

20 

16 

25 

0to36 

Post- 

Normal 

31 

18 

12            26 

0to35 

53 

20 

16 

24.5 

8  to  34 

Seniors 

1 

Seniors 

Pre- 

Normal 

14 

21.25 

16.75 

23.06 

14.25  to  29 

26 

19.25 

17.19 

23 

13.75  to  35.5 

Normal 

48 

20.62 

17.25 

24.94 

-10  to  37.5 

181 

20 

17 

23 

-6  to  37 

Post- 

Normal 

19 

18 

13.5 

20 

-6.5  to  36 

43 

20.25 

18 

24 

14  to  30 

different  college  years.    Inspection  of  the  table  with  its  accompany- 
ing graph  brings  out  these  facts : 

1.  During  the  freshman  and  sophomore  years,  the  pre-normal 
entrants,  both  male  and  female,  showed  the  highest  scholarship,  and 
the  post-normal  entrants  showed  the  lowest. 

2.  The  differences  in  the  achievements  of  these  three  entrance- 
groups  were  most  pronounced  among  the  males. 

3.  During  the  junior  and  seniors  years,  the  achievements  dis- 
played by  the  three  entrance-age  groups  were  more  nearly  identical. 

4.  The  female  seniors  showed  a  slight  tendency  to  reverse  the 
relations  obtaining  during  the  first  two  college  years.  That  is  to 
say,  the  post-normal  entrants  now  displayed  greatest  efficiency,  and 
the  pre-normal  entrants  least. 

5.  All  three  entrance-age  groups  showed  a  general  rise  in  the 
quality  of  the  marks  received,  in  passing  through  the  successive 


NOBMAL,  FEE-NORMAL,  POST-NOBMAL  ENTRANCE  AGES       81 


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82 


THE  SIXTEENTH  YEAEBOOK 


college  years.  This  tendency  is  greatest  in  the  post-normal,  and 
least  in  the  pre-normal  group,  and  most  conspicuous  among  the 
males.    These  facts  stand  out  much  more  clearly  in  Graph  XI. 

6.  Among  the  males  the  post-normal  group  decreased  in  size 
most  rapidly,  and  the  pre-normal  group  least  rapidly,  in  passing 
from  the  freshman  to  the  senior  college  years.  This  tendency  indi- 
cates that  elimination  among  the  males  was  greater  among  the  older 
entrants.  The  problems  of  elimination  will  be  treated  more  at 
length  in  Section  2. 

7.  The  males  showed  a  larger  proportion  than  did  the  females 
in  both  the  pre-normal  and  post-normal  entrance  groups;  which 
agrees  with  a  previous  statement  to  the  effect  that  the  males  showed 
the  greater  variability  in  entrance-ages. 

TABLE    20 

Comparative  Scholarship,  During  Successive  College  Years,  of  Groups  of  Different  Ages 
at   Entrance    Who   Remained   till    Graduation 


Males 

Females 

Age  at 
Entrance 

is 
1 1 

Median 
Schol- 
arship 

Middle  50 
percent 

Range  of 

Scholarship 

Values 

^  1 

Median 

Middle  50 
percent 

Range  of 

1st 

Quar- 

tile 

3d 

Quar- 

tile 

Schol- 
arship 

1st 

Quar- 

tile 

3d 
Quar- 

tile 

Scholarship 
Values 

Freshmen 

Freshmen 

Pre- 

Normal 

14 

18.5 

16 

21.75 

12  to  26 

26 

17 

14.75 

21 

7  to  29 

Normal 

48 

17 

11 

20 

0  to  30 

181 

16 

12 

21.5 

5  to  32 

Post- 

Normal 

19 

15 

11 

21 

-3  to  26 

43 

17 

14 

21 

6  to  33 

Sophomores 

Sophomores 

Pre- 

Normal 

14 

18.5 

15 

22 

11  to  25 

26 

21 

15 

26 

2  to  32 

Normal 

48 

17 

12.25 

22.25 

6  to  37 

181 

17 

14 

24 

4  to  36 

Post- 

Normal 

19 

16 

11 

25 

2  to  29 

43 

18 

14 

24 

7  to  40 

Juniors 

Juniors 

Pre- 

Normal 

14 

20.5 

18 

23.5 

10  to  29 

26 

21 

16.5 

26 

6  to  37 

Normal 

48 

19 

14.25 

26.75 

-4  to  36 

181 

20 

16 

26 

0to36 

Post- 

Normal 

19 

18 

12 

26 

0to35 

43 

21 

16 

25 

8  to  34 

Seniors 

Seniors 

Pre- 

Normal 

14 

21.25 

16.75 

23 

14.25  to  29 

26 

19.25 

17.2 

23 

13.25  to  25.5 

Normal 

48 

20.6 

17.25 

24.9 

-10  to  37.5 

20 

17 

23 

-6  to  37 

Post- 

181 

Normal 

19 

18 

13.5 

20 

-65  to  36 

43 

20.25 

18 

24 

14  to  30 

NORMAL,  FEE-NORMAL,  POST-NORMAL  ENTRANCE  AGES       83 

Let  US  now  contrast  Table  19  and  Graph  X  with  Table  20  and 
Graph  XI.  In  the  latter  we  have  displayed  the  achievements  for 
each  college  year  of  those  males  and  females  only  who  persisted  in 
their  work  until  the  end  of  the  fourth  year.  Table  19  and  Graph  X 
thus  differ  from  Table  20  and  Graph  XI,  in  that  the  latter  pair  ex- 
clude all  those  student  who  were  eliminated  before  the  end  of  the 
fourth  college  year,  while  the  former  pair  include  them.  The  differ- 
ences noted  may  thus  be  attributed  to  elimination. 

Comparison  of  these  graphs  and  tables  brings  out  the  following 
additional  facts: 

8.  In  both  sexes,  the  increase  in  scholarship  shown  in  passing 
from  the  freshman  up  through  the  senior  college  years,  is  due  in 
large  measure  to  the  elimination  of  the  poorest  students  during  each 
successive  year.  This,  statement  is  confirmed  by  reference  to  Table 
21  and  Graph  XII,  in  which  are  represented  the  median  standings 
of  the  pupils  eliminated  from  college  during,  or  at  the  end  of,  each 
collegiate  year. 

9.  Elimination  on  account  of  poor  scholarship  appears  to  have 
been  most  important  as  a  factor  among  the  post-normal  entrants, 
and  among  the  males. 

10.  A  considerable  proportion  of  the  rise  in  scholarship  to  be 
noted  from  year  to  year,  is  apparently  due  to  the  fact  that  upper 
classmen  received  higher  marks  than  lower  classmen,  even  when 
the  same  individual  students  were  concerned  in  each  case. 

11.  Of  the  eliminated  students,  the  females  ranked  generally 
higher  in  scholarship  than  did  the  males;  but  of  the  four-year 
students  the  males  show  practically  equal  achievement,  except  in 
the  post-normal  group. 

Section  2 

comparative  college  efficiency  as  measured  by  retention 
and  elimination 

From  Table  22  and  Graph  XIII,  describing  the  number  of 
semesters  which  the  median  and  quartile  students  of  each  entrance 
group  remained  in  college,  we  derive  the  following  statements : 

1.  The  females  showed  far  less  tendency  than  the  males  to  be 
lost  before  the  end  of  the  college  course. 


84 


TEE  SIXTEENTH  YEARBOOK 


TABLE  21 

Number  of  Students  of  Each  Entrance  Group  Who  ivere  Eliminated  During  or 
at  End  of  Each  College  Year  and  Their  Median  Scholarship 


Age  at 
Entrance 

Male 

Female 

College 
Year 

Number  of  1 

Students           Median 
Eliminated      Scholarship 

Number  of 

Students 
Eliminated 

Median 
Scholarship 

Freshmen 

Pre-Normal 

Normal 
Post-Normal 

7 
59 

47 

0 
6 
1.5 

7 
69 
46 

8 

10 

5 

Sophomores 

Pre-Normal 

Normal 
Post-Normal 

3 
45 
26 

5 
8 
6 

8 
41 
17 

9 
13.5 
21 

Juniors 

Pre-Normal 

Normal 
Post-Normal 

13 
20 
13 

13.5 

14.75 

14 

7 
35 
10 

20 
18 
14.75 

Seniors 

Pre-Normal 

Normal 
Post-Normal 

Not  ascer 

tained 

Not  ascer  tained 

TABLE  22 

Nurnber  of  Semesters  Which  the  Median  Student,  and  the  First  and  Third 
Qvjartile  Students,  of  each  entrance  group,  Memained  in  College. 


Males                         1                       Females 

Age  at 
Entrance 

Semester 

Eetention 

of  Median 

Student 

Semester  Eetention 

of  Middle  50 

percent 

Semester 

Eetention 

of  Median 

Student 

Semester  Eetention 

of  Middle  50 

percent 

1st 
Quartile 

3d 
Quartile 

1st 
Quartile 

3d 
Quartile 

Pre-Normal 

Normal 
Post-Normal 

5.5 

4 

3 

4.25 

2 

2 

8 
8 
5.5 

8 

8 
4 

4 
3 
2 

8 
8 
8 

2.  In  both  sexes,  the  post-normal  entrants  showed  the  least 
degree  of  persistence ;  while  with  the  males  the  pre-normal  entrants 
showed  the  greatest. 

From  inspection  of  Graph  XIV,  entitled  "Percentages  Elimin- 
ated Annually, ' '  we  are  able  to  add  these  facts : 

3.  Among  the  normal  and  post-normal  entrants,  the  greatest 
percentage  of  elimination  occurred  before  the  beginning  of  the 
sophomore  year,  the  next  greatest  before  the  junior  year,  and  the 
third  greatest  before  the  senior  year ;  while  by  far  the  least  drop- 
ping-out  occurred  during  the  senior  year.  This  statement  holds 
for  both  sexes.    The  pre-normals  show  some  alteration  of  this  order, 


NOBMAL,  PBE-NOBMAL,  POST-NOBMAL  ENTBANCE  AGES        85 


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TEE  SIXTEENTH  YEARBOOK 


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NOBMAL,  PBE-NOBMAL,  POST-NOBMAL  ENTBANCE  AGES        87 

but  as  this  group  was  rather  small  numerically,  it  is  not  improbale 
that  the  order  here  is  accidental. 

4.  The  female  normal  entrance-group  shows  a  slightly  greater 
persistence  than  the  p re-normal  group,  when  thus  subjected  to  a 
closer  analysis.  But  the  difference,  while  opposed  to  that  found  in 
the  case  of  the  males,  is  exceedingly  small. 

Returning  now  to  Table  21  and  Graph  XII,  which  are  concerned 
with  the  relation  between  elimination  and  scholarship,  we  find 
authority  for  adding  the  following  to  our  catalogue  of  inferences : 

5.  The  freshmen  who  were  dropped  displayed  exceedingly 
poor  scholarship,  particularly  the  males ;  the  sophomores  who  were 
dropped,  while  very  low,  did  better  work;  the  juniors  who  were 
eliminated  were  nearly  the  equals  in  scholarship  of  those  who  were 
retained.  The  number  of  students  who  were  dropped  during  the 
senior  year  was  too  small  to  warrant  continued  comparison. 

6.  Poor  scholarship  was  apparently  a  more  consistent  com- 
panion of  elimination  among  those  students  who  entered  before  and 
after  normal  age  than  among  those  who  entered  normally.  The 
female  sophomores  and  juniors  show  exception  to  this  statement, 
but  these  are  self -contradictory  in  their  tendencies. 

Section  3 

SUMMARY 

That  the  principal  tendencies  displayed  in  this  chapter  are  com- 
pletely in  harmony  with  those  described  in  Chapter  IV,  may  be 
shown  by  a  few  brief  statements. 

During  the  freshman  and  sophomore  years,  the  pre-normal 
entrants  showed  the  highest  college  efficiency  and  the  post-normal 
entrants  showed  the  lowest.  Little  difference  was  manifested  be- 
tween these  groups  during  the  junior,  and  particularly  the  senior, 
college  years. 

Poor  scholarship  eliminations  were  greatest  in  the  post-normal 
group,  and  least  in  the  normal  group. 

Teachers  gave  increasingly  high  marks  to  the  same  students 
during  successive  college  years.  For  statistical  reasons,  owing  to 
the  elimination  of  the  poorer  students  during  the  earlier  years, 
one  would  expect  the  marks  of  the  group  which  remained  to  de- 
crease rather  than  to  increase  in  median  value  as  time  went  on. 


CHAPTER  VI 

A  PARTIAL  EXPLANATION  OF  THE  RELATIONS  OBTAIN- 
ING BETWEEN  AGE  AT  ENTRANCE  AND 
COLLEGE  EFFICIENCY 

We  have  now  to  seek  an  answer  to  one  main  question :  Why 
were  the  pre-normal  entrants  superior,  and  the  post-normal  en- 
trants inferior  in  college  efficiency  to  the  normal  entrants? 

The  explanation  which  we  shall  advance  starts  from  this 
hypothesis.  The  students  who  entered  college  before  normal  age 
consisted  of  those  students  who  were  graduated  from  the  high 
school  early  because  of  superior  ability,  and  who  would  be  expected 
to  display  corresponding  superiority  in  college.  The  post-normal 
entrants  comprised  at  least  two  groups  of  students ;  first,  those  who 
were  graduated  late  from  the  high  school,  in  most  cases  because  of 
lack  of  interest  or  ability ;  and  second,  those  who  were  graduated 
from  the  high  school  on  schedule  time,  but  who  permitted  an  interval 
of  a  year  or  more  to  elapse  before  entering  college.  The  inferiority 
of  the  post-normal  entrants  was  due  to  the  first,  and  possibly  to 
both,  of  these  groups. 

The  present  chapter  is  devoted  to  the  demonstration  and  appli- 
cation of  this  hypothesis.  Its  demonstration  necessitates  a  com- 
parison between  the  work  done,  both  in  the  high  school  and  the  col- 
lege, by  those  students  who  came  to  college  immediately  from  the 
high  school  and  the  work  done  by  those  who  permitted  an  interval 
to  intervene.  We  shall  accordingly  divide  each  of  the  three  entering 
groups  into  four  sections,  consisting  respectively  of  (1)  those 
students  who  permitted  an  interval  of  time  to  elapse  between  high- 
school  graduation  and  college  entrance,  (2)  those  who  were  gradu- 
ated from  the  high  school  after  normal  age,  but  came  immediately 
to  college,  (3)  those  who  were  graduated  late  from  the  high  school, 
and  entered  college  a  year  or  more  thereafter,  and  (4)  those  who 
did  neither,  but  who,  after  having  been  graduated  on  time,  entered 
college  immediately  thereafter. 

88 


AGE  AT  ENTEANCE  AND  COLLEGE  EFFICIENCY 


89 


Section  1 

normal  and  non-normal  entrance-ages  as  related  to  immediacy 
of  college  entrance 

Let  US  first  note  the  comparative  number  of  normal,  pre-normal, 
and  post-normal  entrants  who  belong  in  each  of  these  divisions. 

TABLE  23 

Comparative  Numbers  of  Students  Entering  College  at  BiSerent  Ages  and  at 
Different  Periods  After  High-School  Graduation, 


Males 


©    O    fl 


1.  With  in- 
tervening 
period 

2.  With  late 
graduation . 

3.  With  both. 

4.  With 
neither .... 

5.  Unknown.  . 


III 

Oh 


Females 


6  o  fl 
(In 


1^1 


Ml 


1          Per- 
No.     cent 

No. 

Per- 
cent 

No. 

Per- 
cent 

No. 

Per- 
cent 

Per- 
No.     cent 

1       2.7 

22 

12.8 

23 

21.9 

5 

10.4 

34     10.4 

.. 

•• 

•• 

58 
7 

17 

55.2 
6.7 

16.2 

41 
2 

85.4 
4.2 

274     84.2 
18       5.5 

32     86.5 
4     10.8 

136 
14 

78.9 
8.3 

No. 


42 
18 


Per- 
cent 


43     37.1 


36.2 
15.5 


13     11.2 


•Certain  features  of  this  table  might  easily  have  been  forecasted. 
No  late  graduates  from  the  high  school  could  be  found  among 
students  who  entered  college  at  or  before  normal  age,  and  none  who 
was  without  either  an  intervening  period  or  a  late  graduation  could 
be  found  in  the  post-normal  group.  But  the  tables  give  us  two  new 
facts  of  considerable  importance.  Of  the  male  post-normals,  more 
were  graduated  from  the  high  school  late  than  entered  college  after 
a  lapse  of  time,  while  of  the  female  post-normals  the  reverse  tends 
to  be  the  case.  Again,  a  larger  proportion  of  the  pre-normals  than 
of  the  normals  of  both  sexes,  entered  directly  from  a  normal-age 
high-school  graduation.  It  should  also  be  noted  that  only  six  cases, 
in  both  sexes,  of  the  pre-normals  permitted  a  year  of  time  to  inter- 
vene before*  college  entrance. 


90 


THE  SIXTEENTH  YEARBOOK 


We  pass  next  to  the  quality  of  scholarship  displayed  by  each 
of  these  groups.  This  item  was  ascertained  for  the  freshman  year 
only — the  year  when  differences  in  scholarship  are  most  manifest 
and  when  all  college  entrants  start  in  competition. 


TABLE  24 

Quality  of  College  Scholarship  Displayed  hy  Students  Entering  at  Different 
Entrance  Ages  and  at  Different  Periods  after  High-School  Graduation 


Pre-normal 
College  Entrants 


Me- 
dian 
schol- 
arship 


Eange  of 

Middle  50 

percent 


Normal 
College  Entrants 


Me- 
dian 
schol- 
arship 


Eange  of 

Middle  50 

percent 


Post-normal 
College  Entrants 


Me- 
dian 
schol- 
I  arship 


Eange  of 

Middle  50 

percent 


Males 


With  interven- 
ing period.  .  . . 
With  late 
graduation .  . . 
With  both.  . .  . 
With  neither. 


17 


13 


8  to  19.5 


16  9  to  21         11 


5  to  18 


16 


9  to  20 


5.5  1-1.25  to  13 
7  -6  to  15 


Females 


1.  With  interven- 
ing period.  .  . . 

2.  With  late 
graduation ... 

3.  With  both 

4.  With  neither. . 


18 


10.5  to  23 


16         11.5  to  19.5       15  10  to  20 


15 


10.75  to  23 


16 

8.5 
10.5 


12  to  21 

5  to  17 

6  to  16.5 


This  table  makes  evident  the  following  points : 

1.  Among  the  pre-normal  entrants  of  both  sexes,  those  pupils 
who  waited  a  year  or  more  after  graduating  from  the  high  school 
before  entering  college,  stood  somewhat  higher  in  their  college  work 
than  did  those  who  did  not  wait.  Here  we  repeat  that  there  were 
only  six  pre-normal  entrants  who  permitted  this  delay. 

2.  The  same  fact  appears  among  the  males  who  entered  at 
normal  age.  Among  the  female  normal  entrants,  the  two  groups 
show  the  same  median,  but  the  range  of  the  middle  50  percent  is 
lower  with  those  who  entered  college  immediately,  than  with  those 
who  waited  a  year  or  longer.  In  these  normal-entrance  groups,  t!ie 
number  of  cases  is  sufficiently  large  to  give  significance  to  the 
results. 


AGE  AT  ENTEANCE  AND  COLLEGE  EFFICIENCY  91 

3.  The  point  which  we  would  especially  emphasize  in  connec- 
tion with  our  present  problem,  is  found  on  inspection  of  the  post- 
normal-entrance  groups.  Here  we  find  that  those  students  who 
were  graduated  from  the  high  school  late,  and  who  for  this  reason 
were  late  entrants  at  college,  stood  lower  than  did  those  who  were 
graduated  from  the  high  school  on  schedule  time  but  who  waited  a 
year  or  longer  before  entering  college.  Those  who  were  graduated 
late,  and  also  permitted  an  intervening  period,  stood  between  the 
groups  just  described. 

4.  The  post-normal  entrants,  who  entered  college  a  year  or 
more  after  graduation,  are  evidently  not  responsible  for  the  general 
inferiority  manifested  by  this  group,  since  in  both  sexes  their  median 
rank  is  above  the  median  ranks  of  the  total  post-normal  and  normal 
groups. 

These  three  results  are  rather  generally  confirmed  when  one 
applies  the  second  of  our  criteria  of  efficiency,  i.  e.,  retention.  The 
post-normal  entrants  showed  the  following  median  semesters  reten- 
tion :  males,  with  intervals,  5.75  semesters ;  males,  with  late  gradu- 
ation, 3  semesters;  females,  with  intervals,  8  semesters;  females, 
with  late  graduation,  5  semesters.  The  pre-normal  females  showed 
a  better  retention  for  those  who  entered  immediately  than  for  those 
who  waited,  but  the  pre-normal  males  who  entered  after  a  wait 
remained  for  college  graduation.  In  the  normal  entrance-age  group 
the  regular  entrants  and  those  who  delayed  before  entrance  show 
the  same  median,  and  the  same  inter-quartile  range. 

These  results  substantiate  that  portion  of  our  hypothesis  which 
relates  to  the  deficiency  characterizing  the  post-normal  entrants. 
These  are  demonstrated  to  consist  of  the  two  ty^es  of  students 
assumed  in  the  hypothesis,  plus  a  third  type  in  which  both  depar- 
tures from  normal  entrance  conditions  are  combined.  Of  these,  stu- 
dents of  the  type  entering  college  late  because  they  were  graduated 
from  the  high  school  behind  schedule,  are  shown  to  be  responsible 
for  the  deficiencies  described. 

It  remains  to  prove  that  the  pre-normal  entrants  did  work  in 
the  high  school  superior  to  that  done  by  the  normal  and  post- 
normal  entrants,  and  were  thus  a  positively  selected  group ;  while 
the  post-normal  entrants  who  were  graduated  late  from  the  high 


92  THE  SIXTEENTH  YEABBOOK 

school  did  inferior  work  there,  and  consequently  were  a  negatively- 
selected  group.  For  this  purpose  we  turn  to  the  high-school  records 
of  the  different  groups  of  students. 

Section  2 

age  and  immediacy  of  college  entrance  as  related  to 
high-school  scholarship 

We  are  able  in  this  connection  to  present  the  high-school  records 
for  only  285  of  the  828  college  entrants  considered,  but  to  secure 
even  these  the  records  of  3644  high-school  seniors  were  examined.  We 
can,  however,  state  the  scholarship  position  among  his  high-school 
classmates  occupied  by  each  of  the  285  college  entrants.  To  deter- 
mine this  position,  the  students  of  each  high-school  graduating  class 
sending  members  to  college  were  ranked  in  order  of  scholarship  from 
highest  to  lowest,  and  divided  into  five  equal  groups,  or  quintiles. 
In  the  table  accompanying  this  section  (Table  25),  this  quintile 
position  is  stated  for  the  median  pupil,  and  for  the  first-  and  third- 
quartile  pupils,  of  each  of  the  groups  entering  college  under  the 
conditions  described  in  Section  1.  As  the  best  of  these  quintiles 
was  numbered  1  and  the  poorest  was  numbered  5,  fhe  smaller  tJie 
figure  representing  the  median  scholarship  of  each  group,  the  better 
tlie  scJiolarsJiip  rank. 

Table  25  affords  the  additional  facts  necessary  to  complete  the 
demonstration  of  our  hypothesis.  The  following  statements  are 
based  upon  it  : 

1.  The  pre-normal  college  entrants  are  seen  to  have  ranked 
notably  higher  in  high-school  scholarship  than  the  normal  and  post- 
normal  entrants.  This  fact  confirms  our  original  assumption  that 
they  were  a  positively  selected  group. 

2.  All  of  the  post-normal  female  entrants  ranked  lower  in  the 
high  school  than  the  normal  and  pre-normal  entrants.  They  were 
thus  all  a  negatively  selected  group.  The  two  chief  types  of  post- 
normal  male  entrants,  the  late  graduates  and  those  entering  after  a 
lapsed  interval,  showed  a  difference  in  high-school  rank  in  favor 
of  the  latter.  No  difference  of  this  kind  is  noticeable  in  the  case 
of  the  females.    These  facts  confirm  our  original  assumption  that  the 


AGE  AT  ENTRANCE  AND  COLLEGE  EFFICIENCY 


93 


TABLE  25 

High-School  Scholarship  (in  Terms  of  Quintile  Distribution)  of  285  High-School 

Graduates  Entering  College  at  Different  Ages  and  at  Different  Periods 

after  High  School  Graduation 


Pre-normal 
College  Entrants 


Me- 
dian 
schol- 
arship 


Eange  of 

Middle  50 

percent 


Normal 
College  Entrants 


Me- 
dian 
schol- 
arship 


Range  of 

Middle  50 

percent 


Post-normal 
College  Entrants 

Me- 

dian 
schol- 
arship 


Eange  of 

Middle  50 

percent 


Males 


1.  V/ith  interven 
ing  period 

2.  With  late 
graduation 

3.  With  both 

4.  With  neither .  . 


2.7 


1.7  to  4 


4.3 


1.5  to  5 


3.1        1.7  to  4.4 


3.2 
2.5 


2  to  4 

1.5  to  3.8 
2  to  3.25 


Females 

1.  With  interven 

ing  period 

3 

2.5 

1.6  to  3.7 

2.7 

2  to  4 

2.  With  late 

graduation 

2.7 

2  to  4.3 

3.  With  both 

, . 

. . 



3 

4.  With  neither.  . 

1.9 

1.5  to  3.7 

2.1 

1.8  to  3.1 

post-normal  entrants  who  were  graduated  from  the  high  school 
late  were  a  negatively  selected  group. 

3.  It  should  also  be  remarked  that,  in  general,  those  students 
who  entered  college  after  a  lapse  of  time,  came  from  a  poorer  type 
of  high-school  graduates  than  did  those  who  entered  immediately 
after  graduation.  We  have  already  seen  (Table  24)  that  these 
elapsed-interval  students  did  a  better  grade  of  work  in  college. 
These  facts  suggest  that  such  an  interval  contributed  to  better 
college  work.  However,  as  the  students  in  the  two  cases  are  not 
absolutely  identical, — the  earlier  tables  including  many  not  included 
in  the  last — we  must  await  the  results  disclosed  in  the  next  section. 


Section  3 

comparison  of  the  achievements  of  identical  students  in  the 
high  school  and  college 

Thus  far  we  have  seen  (1)  that  the  pre-normal  college  entrants 
did  a  better  grade  of  work,  both  in  the  high  school  and  college,  than 


94 


THE  SIXTEENTH  YEAEBOOK 


the  normal  and  post-normal  entrants;  and  (2)  that  the  post-normal 
college  entrants  who  had  been  graduated  late  from  the  high  school, 
shower  inferior  scholarship,  both  in  college  and  high  school.  In 
other  words,  the  college  superiority  of  the  pre-normal  entrants  and 
the  college  inferiority  of  the  post-normal  entrants,  is  due  to  the  type 
of  high-school  student  mainly  selected  by  each  group.  But  there 
is  one  defect  in  our  proof  thus  far ;  the  students  for  whom  the  high- 
school  records  are  given  constitute  only  a  portion  of  those  for  whom 
the  college  records  are  given.  In  the  following  table,  therefore,  is 
stated  the  collegiate  scholarship  of  identically  the  same  students  as 
those  whose  high-school  scholarship  is  presented  in  Table  25. 


TABLE  26 

College  Scholarship  of  S85  High-School  Graduates  Entering  College  at  Different 
Ages  and  at  Different  Periods  after  High-School  Graduation 

Pre-normal 
College  Entrants 

Normal 
College  Entrants 

Post-normal 
College  Entrants 

Me- 
dian 
schol- 
arship 

Eange  of 

Middle  50 

percent 

Me- 
dian 
schol- 
arship 

Eange  of 

Middle  50 

percent 

Me- 
dian 
schol- 
arship 

Eange  of 

Middle  50 

percent 

Males 

1.  With  interven- 
ing period .... 

2.  With  late 
graduation 

3.  With  both 

4.  With  neither.  . 

ii 

7  to  18 

16 

10 

3  to  17 

4  to  17 

12 

5.5 

8.5 

10  to  19 
-6  to  14.75 

Femfiales 

1.  With  interven- 
ing period 

2.  With  late 
graduation .... 

3.  With  both 

4.  With  neither.  . 

10 
14 

*8  to  17.75 

16 
ii 

12.5  to  24.25 

V  to  18 

14 

7 
14 

11.5  to  19 
5  to  14.5 

Comparison  of  this  table  with  Table  24  shows  that  it  reveals 
practically  the  same  tendencies,  and  warrants  the  statement  that 
the  high-school  records  displayed  in  Table  25  are  representative, 
even  if  incomplete. 


AGE  AT  ENTBANCE  AND  COLLEGE  EFFICIENCY  93 

Section  4 
conclusions 

The  main  conclusions  which  we  would  state  once  more  are  these : 
First,  students  who  entered  the  college  at  ages  younger  than  normal 
entrance  age  stood  higher  and  remained  longer,  upon  the  whole 
than  those  who  entered  normally  or  older.  Second,  students  who 
entered  at  older  than  normal  ages,  stood  lower  and  remained  for  a 
shorter  period  than  those  who  entered  at  normal  age  or  younger. 
Third,  the  18-year-old  normal  entrants  outstayed  and  outranked 
the  19-year-old  normal  entrants,  and  there  is  evidence  that  the 
post-normals  who  entered  after  22  or  23  were  somewhat  more 
efficient  than  the  younger  entrants  of  the  same  group. 

Do  these  statements  mean  that  pressure  should  be  exerted 
to  force  all  prospective  students  into  college  before  they  are  18 
years  of  age?  Ought  what  we  have  described  as  'pre-normal* 
to  become  the  'normal'  entrance  ages?  Such  a  conclusion  would 
be  most  ill-advised.  Complete  investigation  shows  that  those 
students  who  entered  college  before  18  years  of  age  were  a  selected 
group,  who  had  finished  the  high  school  before  the  majority  of  their 
fellows  because  of  superior  ability,  and  who,  accordingly,  would  be 
expected  to  surpass  them  in  college.  Owing  to  the  high  correlation 
shown  to  obtain  between  retention  and  good  scholarship,  they  would 
also  be  expected  to  show  greater  persistence.  A  majority  of  the 
post-normal  entrants,  on  the  other  hand,  are  shown  to  have  been 
poor  students  in  the  high  school,  and  for  this  reason  to  have  been 
graduated  therefrom  at  a  comparatively  late  age.  These  students 
naturally  would  be  slow  and  uncertain  quantities  in  college.  Selec- 
tion, not  age,  is  the  real  key  to  the  situation. 

But  if  the  demonstrated  superiority  of  the  early  over  the  late 
entrants  cannot  be  urged  as  an  argument  that  all  students  should 
enter  college  before  18,  cannot  the  inferiority  of  the  late  entrants 
at  least  be  urged  to  prevent  those  seemingly  waste  intervals  which 
students  often  permit  to  elapse  between  high-school  graduation  and 
the  taking  up  of  college  work?  Here,  again,  our  answer  must  be 
negative.  The  inferiority  of  these  late  entrants  was  clearly  due  to 
the  poor  students  who  made  up  a  large  part  of  the  group,  and  not 


96  THE  SIXTEENTH  YEARBOOK 

intrinsically  to  age.  Furthermore,  in  the  normal  entrance  group 
those  students  who  entered  college  a  year  or  more  after  high-school 
graduation  generally  outranked  those  who  entered  immediately,  in 
spite  of  the  fact  that  they  were  apparently  inferior  students  in  the 
high  school.  Here  the  interval  seemed  in  reality  to  contribute  to 
college  efficiency. 

The  second  conclusion  of  general  interest  which  we  wish  again 
to  emphasize,  relates  to  the  better  standard  of  scholarship  displayed 
in  passing  from  the  first  to  the  last  college  year.  Two  causes  of  this 
elevation  in  standards  are  clearly  indicated.  The  first  and  most 
effective  is  the  elimination  of  inefficient  students,  particularly  dur- 
ing the  first  two  college  years.  But  the  second,  to  which  we  would 
call  particular  attention,  is  the  actually  increasing  generosity  of 
teachers  in  the  distribution  of  high  marks,  clearly  shown  by  the 
fact  that  the  same  group  of  students  received  higher  and  higher 
grades  from  year  to  year.  This  fact  is  important  as  it  indicates 
that  the  standard  of  work  required  during  the  successive  college 
years  did  not  rise  in  proportion  to  the  rise  in  student  ability.  A 
proportional  rise  of  this  sort  has  been  assumed,  by  those  who 
advocate  the  normal  curve  as  the  criterion  of  a  proper  distribution 
of  marks. 

There  is  yet  a  third  conclusion  to  which  the  reader 's  attention 
may  profitably  return.  Several  students  of  the  problem  of  marking 
have  shown  that,  in  both  the  elementary  and  the  high  school,  female 
pupils  received  higher  marks  than  male  pupils.  Our  data  show 
that  the  same  relations  exist  in  college.  But  when  we  consider  sep- 
arately the  males  and  females  who  spent  four  full  years  at  college 
work,  we  discover  that  the  difference  has  practically  disappeared. 

Two  facts  thus  demand  interpretation.  As  to  the  first,  that, 
in  general,  the  males  received  lower  marks  than  the  females,  here, 
as  in  the  earlier  studies,  we  must  beware  of  an  interpretation  which 
consigns  either  sex  to  the  limbo  of  inferior  ability.  Doubtless  several 
factors  cooperate  to  produce  this  consistently  appearing  relation, 
and  possibly  not  least  among  them  is  the  better  adaptation  of  our 
entire  school  system,  from  top  to  bottom,  to  the  peculiar  interests 
and  abilities  of  the  female  sex.  But  upon  this  important  question  of 
^causes  our  study  throws  no  light,  and  we  must  content  ourselves 


AGE  AT  ENTBANCE  AND  COLLEGE  EFFICIENCY  97 

with  the  mere  confirmation  of  results  already  sufficiently  proved  by 
others. 

The  second  fact,  that  the  continuous  four-year  students  of  the 
two  sexes  showed  practically  equal  efficiency,  has  not  previously 
come  to  the  writer's  notice.  Its  full  significance  is  not  clear,  but 
it  possibly  is  no  more  than  an  indication  that  elimination  had  suc- 
cessfully removed  the  misfits  of  both  sexes,  and  had  left  chiefly 
those  who  were  peculiarly  adapted  to  college  life.  These  students 
were  in  all  probability  too  much  the  product  of  an  artificial  selection 
to  be  representative  of  the  usual  abilities  or  achievements  of  either 
sex. 


CHAPTER  VII 

SIZE  OF  HIGH  SCHOOL  AS  RELATED  TO  EFFICIENCY 

IN  COLLEGE 

Is  there  any  consistent  relation  between  the  number  of  pupils 
enroled  in  the  different  high  schools  tribi:^tary  to  the  university 
under  discussion  and  the  scholarship  and  persistence  shown  in  col- 
lege by  their  graduates? 

The  methods  used"  in  attempting  to  reach  a  solution  of  this 
problem,  are  fundamentally  like  those  followed  in  the  study  of  en- 
trance ages.  The  main  difference  is  that  size  of  high  school,  rather 
than  age  at  entrance,  is  used  to  determine  membership  in  the 
student  groups  whose  college  efficiency  is  to  be  compared.  There 
are  six  of  these  groups  of  public-school  graduates,  consisting  respec- 
tively of  those  representing  high  schools  with  enrolments  of  (1)  100 
pupils  or  less,  (2)  101  to  200  pupils,  (3)  201  to  300  pupils,  (4) 
301  to  500  pupils,  (5)  501  to  1000  pupils,  and (6)  more  than  1000 
pupils.  This  grouping  was  borrowed  from  Counts^  and  from  Jessup 
and  Coffman^  in  order  that  our  results  might  be  made  comparable 
with  theirs.  To  these  six  groups  we  have  added  two  others,  not 
included  in  the  earlier  studies,  consisting  of  the  graduates  of  (7) 
military  and  (8)  private  schools,  including  schools  maintained  by 
religious  orders. 

Section  1 

size  op  high  school  as  related  to  college  scholarship 

The  relation  between  size  of  high  school  and  the  college  scholar- 
ship of  high-school  graduates,  is  shown  in  Tables  27  and  28.  And 
Graph  XV.  These  tables  and  this  graph  are  formulated  according 
to  the  plan  already  employed  in  Chapter  IV,  and  should  be  inter- 
preted similarly.    They  warrant  these  conclusions : 


^Judd,  C.  H.,  and  Counts,  G.  S.  Study  of  the  Colleges  and  High  Schools 
of  the  North  Central  Association.    Bulletin  Bureau  of  Education,  1915.  No.  6. 

-Jessup,  W.  A.  and  Coffman,  L.  D.  North  Central  High  Schools.  13th 
Year-Boole  of  This  Society,  1914,  pp.  73-115. 


SIZE  OF  HIGH  SCHOOL  AS  BELATED  TO  COLLEGE 


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THE  SIXTEENTH  YEARBOOK 


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Private 

SIZE  OF  HIGH  SCHOOL  AS^  MfiUTtB^.  ^0'C(^IiLEGE.  101 

1.  In  the  case  of  males,  military-school  graduates  show  in  the 
freshman  year  the  poorest  general  scholarship  in  college,  private- 
school  graduates  come  next,  and  the  college  scholarship  of  public- 
school  graduates  is  generally  higher  in  the  product  of  the  larger 
than  of  the  smaller  schools. 

2.  The  same  general  tendency  appears  among  the  females, 
except  that  a  deficiency  is  noticed  in  the  graduates  of  schools  enrol- 
ing more  than  1000  pupils.  The  probable  explanation  is  that,  as 
all  of  the  schools  of  this  size  were  local  (Minneapolis  schools),  a 
larger  proportion  of  all  their  female  graduates,  and  hence  of  their 
inferior  female  graduates,  entered  the  university.  A  correspond- 
ing decline  of  the  college  scholarship  curve  would  be  expected. 

3.  In  both  sexes  the  above  described  tendencies  are  largely 
lacking  in  the  last  two  college  years,  when  the  curves  show  great 
irregularity.  This  change  is  clearly  due  to  elimination,  which  fac- 
tor will  next  be  described.  Meanwhile,  the  reader  must  bear  in 
mind  that  freshman  scholarship  alone  bears  directly  upon  our  prob- 
lem. 

Section  2 

SIZE  OF  HIGH  SCHOOL  AS  RELATED  TO  COLIjEGE  RETENTION. 

Table  29  shows  the  percentages  of  college  students  entering 
from  high  schools  of  different  enrolments  who  were  retained  from 
year  to  year.     These  data  appear  again  in  Graph  XVI. 


TABLE  29 


Betention 

in  Percentages  of  Students  Entering  College  from  Military 

and  Pri- 

vate  Schools, 

and  from  Tuhlic  Schools  of  Different  Enrolments 

Males 

Females 

Type  and 
Size  of 

Percent 

Percent 

Percent 

Percent 

Percent 

Percent 

Eetained 

Eetained 

Eetained 

Eetained 

Eetained 

Eetained 

School 

as  Soph- 

as 

as 

as  Soph- 

as 

as 

omores 

Juniors 

Seniors 

omores 

Juniors 

Seniors 

1-100 

54.3 

33.9 

13.6 

79.3 

60.3 

48.3 

101-200 

74.5 

43.1 

19.6 

75.8 

64.5 

59.7 

201-300 

71.4 

38.1 

19.0 

79.3 

58.6 

44.8 

301-500 

501-1000 

65.2 

34.7 

30.4 

88.9 

72.2 

66.7 

1001+ 

68.3 

47.6 

34.1 

75.0 

62.5 

50.0 

Private 

72.7 

45.4 

36.4 

50.0 

40.6 

28.1 

Military 

50:0 

25.0 

12.5 

... 

102  ^.  .v  -;U^#I?^/S:^^^JSJ\J^H  YEARBOOK 


^-t4':/*u|jo-ix/':3  9  -4^. 


SIZE  OF  HIGH  SCHOOL  AS  BELATED  TO  COLLEGE 


103 


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Z0l'3Oo 


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Vf^rof^n-fQ^iata^ci  ^oi;r  ^fars 


GEAPH  XVI. 


Comparative  College  Eetention  of  Students  Entering  from  Military  and 

j^RiVATE  Schools  and  from  Public  High  Schools  of 

Different  Enrolments. 


1.  For  the  males  the  private  schools  showed  the  largest  retention 
of  students  to  the  fourth  college  year.  This  persistence  is  surpris- 
ing in  view  of  the  fact  that  graduates  of  these  schools  showed  infer- 
ior  scholarship  in  college.  However,  the  military-school  graduates 
showed  the  smallest  percentage  of  retention,  as  well  as  the  lowest 
scholarship;  while  of  the  public-school  graduates,  those  from  the 
larger  schools  showed  a  higher  retention  than  did  those  from  the 
smaller  schools. 

2.  For  the  females  the  private-school  graduates  showed  the 
smallest  percentage  of  retention.     Public-school  graduates  showed 


104  THE  SIXTEENTH  TEABBOOK 

in  general  the  tendency  just  described  for  the  males,  but  less  con- 
sistently. Notable  exceptions  are  seen  in  the  groups  representing 
school  populations  of  201  to  300  and  of  ''over  1000."  Reference  to 
Graph  XV  recalls  the  fact  that  these  groups  were  also  deficient  in 
scholarship.  The  deficiency  in  the  ''more  than  1000"  group  has 
been  accounted  for,  but  the  cause  of  the  deficiency,  both  in  scholar- 
ship and  retention,  in  the  201  to  300  pupil  group  is  obscure. 

While  there  are  obvious  discrepancies  in  both  sex-curves,  prob- 
ably owing  to  insufficient  cases,  the  net  result  agrees  with  the  prin- 
ciple already  advanced  that  inferior  scholarship  is  closely  correlated 
with  low  retention  and  high  elimination. 

Section  3 
size  of  high  school  as  related  to  high-school  scholarship. 

The  evidence  which  has  been  advanced  shows  quite  clearly  that 
public-school  graduates  showed  greater  efficiency  in  college  than 
did  the  military-  and  private-school  product,  and  that  the  graduates 
of  the  larger  schools  did  better  work  than  the  graduates  of  the 
smaller  schools. 

A  new  problem  now  confronts  us.  Was  the  greater  college  effi- 
ciency of  the  graduates  of  some  schools  due  to  an  actual  superiority 
of  those  schools  as  college-preparatory  institutions,  or  can  the  phe- 
nomena be  accounted  for  as  the  outcome  of  selection  ?  It  is  possible 
that  the  students  representing  the  larger  public  schools  were  among 
the  best  products  of  those  schools,  while  the  smaller  public  school, 
and  the  private  and  military  schools,  were  represented  more  largely 
by  their  inferior  product. 

A  clear  solution  of  this  issue  can  come  only  from  a  study  of 
the  high-school  rankings  of  the  graduates  of  the  respective  schools. 
As  much  of  such  a  study  as  it  is  possible  for  us  to  make  appears  in 
Table  30.  Unfortunately,  the  number  of  students  for  whom  these 
records  were  obtained  is  small  as  compared  with  the  total  number 
of  college  students.  For  this  reason.  Table  31  is  introduced,  to 
portray  the  college  scholarship  of  the  same  students  whose  high- 
school  ranking  is  set  forth  in  Table  30. 

Table  30  corresponds  to  Table  25  in  Chapter  VI.  Here  as 
there,  and  for  the  same  reason,  tJie  smaller  fhe  rank  value  appearing 


SIZE  OF  EIGE  SCHOOL  AS  BELATED  TO  COLLEGE  105 

in  the  columns  for  the  median  and  the  first  and  third  quartile  pupils, 
tJie  better  the  scholarship  rank. 

Inspection  of  Tables  30  and  31  furnishes  no  conclusive  answer 
to  our  question.  It  is  clear  that  while  the  private  schools  were  rep- 
resented by  their  best  product,  their  graduates  did  very  inferior 
work  in  college.  Private  schools  seem,  therefore,  to  be  inferior  to 
public  schools  as  college-preparatory  institutions. 

But  the  different  groups  of  public-school  graduates  show  no 
clear  tendencies.  An  insufficient  number  of  cases  is  the  probable 
cause.  In  general,  it  appears  that  the  larger  schools  sent  a  slightly 
better  grade  of  their  students  to  college  than  did  the  smaller  schools. 
If  this  be  correct,  then  the  college  superiority  of  the  larger-school 
graduates  may  be  due  partly  or  wholly  to  this  selection,  and  not  to 
the  inferior  efficiency  of  the  smaller  schools.  However,  the  tenden- 
cies here  displayed  are  not  consistent,  and  the  data  are  clearly 
insufficient.  The  writer  accordingly  lays  no  stress  upon  these 
tables. 

Section  4 

size  of  class  in  high  school  as  related  to  college  efficiency 

It  is  popularly  supposed  that  size  of  class  is  a  matter  of 
considerable  importance  in  determining  the  quality  of  school 
instruction.  We  have  therefore  sought  to  discover  any  relation- 
ship which  might  obtain  between  size  of  class  in  high  school  and 
the  later  college  work  of  high-school  graduates. 

The  same  problem  has  been  attacked  from  a  different  angle 
by  several  writers. 

Command  in  1909,  reached  the  conclusion  that  the  size  of  the 
recitation  group  was  not  an  important  factor  in  deportment  nor  in 
the  quality  of  the  daily  work.  Bachman^  and  Boyer^  agree  that  large 
classes  did  not  affect  the  promotion  rate  to  any  noticeable  degree. 


'Cornman,  O.  P.  Effect  of  size  of  class  on  school  progress.  Psychological 
Clinic,  Dec,  1909. 

"Bachman,  F.  P.  Beport  of  N.  Y.  Committee  on  School  Inquiry,  Vol.  I, 
Part  II. 

''Boyer,  P.  A.  Size  of  class  and  promotion  rate.  Psychological  Clinic, 
May,  1914. 


10(5  TEE  SIXTEENTH  YEARBOOK 

Rice^  reached  the  conclusion  that  ''large  classes  ranked  high  as 
often  as  small  classes  when  tested  for  arithmetical  abilities. "  In  a 
recent  study  embracing  1348  classes  and  35,573  pupils,  Harlan"^ 
comes  to  the  following  conclusions : 

"  (1)  The  effect  of  the  size  of  the  class  on  promotion  rate,  though  slight, 
is  in  favor  of  30  pupils  or  less. 

*'  (2)     Large  classes  seem  to  be  a  factor  in  producing  withdrawals 

"  (3)  Medium  sized  classes  (30  to  45  pupils)  seem  to  do  better  work  in 
arithmetic  than  either  very  large  or  very  small  classes. 

'.*  (4)  The  opportunity  of  the  pupils  to  participate  in  the  work  of  the 
recitation  is  somewhat  more  limited  in  large  than  in  small  classes. 

"  (5)  In  the  results  obtained  from  the  data  at  hand  the  efficiency  of  large 
classes  over  that  of  small  classes  is  not  apparent  when  measured  by  the  attention 
given  during  the  recitation,  by  the  time  spent  in  routine  activities  of  the  class- 
room, and  by  the  time  wasted  in  the  study  period. 

*'In  the  light  of  these  conclusions  the  class  of  median  size  (23  pupils) 
seems  too  small  for  the  most  economical  administration  of  our  schools.  Small 
classes  are  expensive  since  they  increase  the  cost  per  pupil.     This  added  expense 

does  not  seem  justified If  one  wishes  to  secure  higher  promotion  rates, 

higher  scores  in  arithmetic,  better  attention  and  wider  participation  in  class 
work,  more  efficient  class  management  and  better  study  habits,  these  things  can 
undoubtedly  be  secured  through  improved  methods  of  instruction  and  more 
efficient  supervision  of  the  larger  classes  rather  than  through  a  reduction  in  the 
size  of  class." 

It  is  almost  axiomatic  to  say  that  a  very  high  correlation  exists 
between  the  number  of  pupils  per  teacher  in  any  school  and  the  gen- 
eral size  of  the  classes  in  that  school.  If  evidence  be  regarded  as 
essential  upon  this  matter,  it  may  be  found  in  the  bulletin  by  Counts 
to  which  wx  have  several  times  referred.  We  are  able  to  present  a 
grouping  of  the  graduates  of  the  various  high  schools  involved  in 
this  study  in  terms  of  the  number  of  pupils  per  teacher  in  each 
school.  Five  classes  have  thus  been  formed,  consisting  of  the  rep- 
resentatives of  (1)  schools  enroling  15  or  fewer  pupils  per  teacher, 
(2)  schools  with  from  16  to  20  pupils,  (3)  those  with  from  21  to  25 
pupils,  (4)  those  with  from  26  to  30  pupils,  and  (5)  schools  with 
more  than  30  pupils  per  teacher.  The  last  group  was  not  further 
divided,  because  there  were  few  representatives  from  schools  with 
more  than  35  pupils  per  teacher,  and  nearly  all  of  these  were  in  one 
school  in  which  the  number  per  teacher  was  36. 


*Rice,  J.  M.     Scientific  Management  in  Education.     Chapter  IV. 
'Harlan,   Chas.   L.      Size    of   class    as   a   factor    in   schoolroom    efficiency. 
Educational  Administration  and  Supervision,  March,  1915. 


SIZE  OF  HIGH  SCHOOL  AS  BELATED  TO  COLLEGE 


107 


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108 


THE  SIXTEENTH  YEABBOOK 


In  studying  the  effect  of  class-size  it  is  necessary  to  exclude  the 
factor  of  size  of  school.  Counts  and  others  have  shown  that  large 
schools  generally  mean  large  classes,  and  it  is  clear  from  earlier 
sections  of  this  chapter  that  the  product  of  the  larger  schools  shows 
the  greater  college  efficiency.  The  presence  of  this  factor,  there- 
fore, would  tell  for  the  superiority  of  large  classes. 

This  disturbing  factor  can  be  practically  eliminated  by  retain- 
ing the  six  groupings  of  schools  already  made  upon  the  basis  of 


TABLE  32 

Belation  hetiveen  Scholarship  of  College  Students  and  the  Number  of  Pupils 

per  Teacher  in  the  High  Schools  from  Which  They  Come 

Both  Sexes  Comlined. 


High 

Pupils 
per 

Number 
of 

Median 
Scholar- 

Middle 50  Percent 

Eange  of 

School 

1st 

3d 

Scholarship 

Enrolment 

Teacher 

Students 

ship 

Quartile 

Quartile 

Values 

1-15 

29 

11 

5.0 

18.0 

-8  to  29 

16-20 

23 

11 

6.0 

15.0 

-8  to  28 

1-100 

21-25 

38 

10.5 

7.7 

14.0 

-8  to  29 

26-30 

17 

11 

4.5 

16.0 

-8  to  19 

31+ 

8 

14.5 

8.5 

21.3 

8  to  26 

1-15 

9 

13 

7.0 

22.5 

6  to  27 

16-20 

32 

11 

6.3 

18.0 

-10  to  28 

101-200 

21-25 

39 

11 

7.0 

16.0 

-6  to  27 

26-30 

23 

15 

4.0 

18.0 

-6  to  28 

31+ 

11 

12 

6.0 

15.0 

-2  to  20 

1-15 

16-20 

1 

-2 

201-300 

21-25 

21 

12 

8.0 

15.5 

-6  to  22 

26-30 

18 

17 

11.3 

19.3 

4  to  25 

31+ 

8 

16 

14.3 

24.5 

11  to  25 

1-15 

. . 

16-20 

3 

9 

7  to  20 

301-500 

21-25 

65 

16 

9.0 

18.5 

-2  to  30 

26-30 

9 

15 

5.5 

16.0 

-6  to  20 

31+ 

2 

13 

11  to  15 

1-15 

. . 

, . 

. . . 

16-20 

1 

-5 

12  to  20 

501-1000 

21-25 

2 

16 

-6  to  25 

26-30 

24 

14.5 

8.8 

19.8 

10  to  14 

31+ 

2 

12 

1-15 



16-20 

lOOO-f 

21-25 

26-30 

7 

21 

8.0 

28.0 

-2  to  28 

31+ 

282 

15 

8.5 

20.0 

-8  to  32 

SIZE  OF  HIGH  SCHOOL  AS  BELATED  TO  COLLEGE  109 

enrolment,  and  by  then  dividing  each  of  these  groups  into  five 
smaller  groups  according  to  the  number  of  pupils  per  teacher.  This 
procedure  yields  Table  32,  which  is  self-explanatory. 

The  table  shows  a  few  consistent  tendencies.  The  "26  to  30 
pupils-per- teacher"  group  seems  generally  to  lead  the  others,  with 
occasional  exceptions  in  favor  of  the  '*  21  to  25"  and  the  '*31-plus" 
groups.  In  general,  the  schools  with  more  than  20  pupils  per 
teacher,  and  less  than  31,  lead  those  with  20  or  fewer,  and  with  more 
than  31.  It  seemes  safe  to  say,  therefore,  that  high-school  gradu- 
ates coming  from  schools  enroling  more  than  20  and  fewer  than  31 
pupils  per  teacher  do  a  better  grade  of  work  in  college,  than  those 
coming  from  schools  with  smaller  or  larger  classes,  irrespective  of 
the  total  enrolment  of  the  schools. 

One  other  conclusion  follows  from  inspection  of  the  table. 
Schools  enroling  fewer  than  200  pupils  show  a  greater  range  in  the 
number  of  pupils  per  teacher,  than  do  the  schools  enroling  more 
than  that  number.  In  general,  also,  the  smaller  schools  are  marked 
by  smaller  classes,  and  the  larger  schools  by  larger  classes — a  result 
which  corroborates  the  findings  of  other  workers. 

Section  4 

SUMMARY 

1.  Graduates  of  military  and  private  schools  show  a  college 
efficiency  inferior  to  that  displayed  by  public-school  graduates. 

2.  Among  public-school  graduates,  the  better  marks  and  the 
greater  retention  are  found  in  the  product  of  the  larger  schools. 

3.  The  inferiority  in  college  of  the  private-school  graduates 
is  clearly  due  to  the  inferiority  of  the  private  school  as  a  college- 
preparatory  institution. 

4.  So  far  as  our  data  go,  the  superiority  shown  in  college  by 
the  graduates  of  the  larger  over  those  of  the  smaller  schools,  may 
or  may  not  be  due  to  the  superiority  of  the  larger  schools  as  college 
preparatory  institutions.  At  present  we  can  only  conclude  that, 
whatever  the  reason,  graduates  of  the  larger  high  schools  may  be 
expected  slightly  to  surpass  the  graduates  of  the  smaller  high 
schools,  when  both  reach  college. 


110  THE  SIXTEENTH  YEARBOOK 

5.  Irrespective  of  the  total  enrolment,  graduates  of  high 
schools  enroling  more  than  20  and  fewer  than  31  pupils  per  teacher 
earn  better  marks  in  college  than  the  graduates  of  schools  enroling 
20  pupils  or  less,  or  more  than  30  pupils  per  teacher.  Within  the 
limits  of  the  study,  therefore,  the  evidence  favors  the  product  of 
classes  ranging  from  21  to  30  pupils. 


CHAPTER  VIII 
GENERAL  SUMMARY 

The  following  statements  are  fairly  derived  from  the  evidence 
which  has  preceded. 

1.  High-school  graduates  who  entered  college  before  18  years 
of  age  did  better  work  and  remained  longer  in  school  than  those 
who  entered  at  18  or  later.  Graduates  who  entered  after  19  years 
of  age  did  poorer  work  and  left  school  earlier  than  did  those  who 
entered  at  19  or  younger.  There  were,  of  course,  numerous  indi- 
vidual exceptions  to  both  statements. 

These  statements  do  not  mean  that  all  high-school  students 
should  be  hurried  into  college  before  18  or,  at  the  latest,  20  years  of 
age.  The  superior  college  efficiency  of  the  younger  entrants  was 
correlated  with  their  superior  efficiency  in  the  high  school,  which 
was  responsible  for  their  early  graduation  therefrom,  and  early 
entry  into  college.  Conversely,  the  college  inferiority  of  the  late 
entrants  was  correlated  with  late  graduation  from  high  school,  be- 
cause of  the  inefficiency  which  they  showed  there.  All  that  can  be 
said  with  confidence  as  a  result  of  this  investigation,  is  that  the 
college  may  expect  in  general  that  its  younger  entrants  will  stay 
longer  than  its  older  entrants  and  will  do  a  superior  grade  of  work. 

2.  Graduates  of  public  schools  did  better  work  in  college  than 
graduates  of  military,  private,  and  church  schools.  In  general,  they 
also  tended  to  remain  longer.  Private  and  church  schools  were 
clearly  inferior  to  public  schools  as  college-prepartory  institutions. 

3.  Graduates  of  the  large  public  schools,  speaking  in  terms  of 
enrolment,  showed  greater  college  efficiency,  both  in  marks  and 
retention,  than  did  graduates  of  the  smaller  public  schools.  It  is 
not  clear  to  what  extent  selection  was  responsible  for  this  difference, 
nor,  on  the  other  hand,  to  what  extent  the  larger  schools  were  the 
better  preparatory  institutions.  In  general,  the  larger  the  schools 
the  greater  was  the  college  efficiency  of  its  graduates;  this  seems 
to  have  been  the  rule. 

Ill 


112  TRE  SIXTEENTH  YEARBOOK 

4.  Schools  enroling  from  21  to  30  pupils  per  teacher  seemed 
to  produce  better  college  students  than  schools  with  fewer  or  with 
more  pupils  per  teacher.  This  result  is  somewhat  different  from 
that  reached  by  other  students  of  the  same  problem,  who  found 
either  no  difference  whatever  in  the  efficiency  of  classes  of  different 
size,  or  a  difference  favoring  classes  of  about  30.  It  should  be 
noted  that  the  present  study  has  eliminated  the  factor  of  size  of 
school,  which,  because  large  schools  mean  large  classes,  and  because 
large  schools  mean  greater  efficiency,  is  a  factor  tending  to  distort 
the  value  of  large  classes. 

5.  The  superiority  of  the  female  entrants  over  the  males,  in 
both  scholarship  and  retention,  appears  throughout  the  study.  The 
students  of  the  two  sexes  who  finished  the  college  course,  however, 
showed  little  difference  in  scholarship  at  any  point. 

6.  The  teachers  of  the  advanced  college  classes  of  the  junior 
and  senior  years  gave  better  marks  than  were  given  by  the  teachers 
in  the  freshman  and  sophomore  years  to  the  very  same  pupils. 
Statistically,  these  pupils  should,  if  anything,  have  received  lower 
marks  on  the  average  during  the  later  years,  owing  to  the  elimination 
of  poor  students  during  the  first  two  years.  It  is  clear  that  scholar- 
ship standards  did  not  rise  proportionally  with  the  increase  in 
student  ability  through  elimination.  Such  a  rise  in  standards  is 
assumed  to  obtain  by  those  who  advocate  the  distribution  of  marks 
according  to  the  normal  curve  throughout  the  college  course. 

7.  There  is  some  evidence,  though  insufficient  for  anything 
approaching  conclusive  proof,  that  the  lapse  of  an  interval  of  a 
year  or  more  between  high-school  graduation  and  college  entrance 
contributed  to  greater  efficiency  when  college  was  once  entered. 

8.  Elimination  from  college  was  highly  qualitative;  the  good 
students  tended  to  remain  and  the  poor  ones  to  go.  This  qualitative 
elimination  was  greatest  in  the  freshman  year,  less  but  still  import- 
ant in  the  sophomore  year,  and  insignificant  in  the  junior  and 
senior  years. 


^C  040/6' 


1 


!f;- 


